Optical System for Ophthalmic Surgical Laser

ABSTRACT

A laser system for ophthalmic surgery includes a laser source to produce a surgical pulsed laser beam, an XY scanner to XY scan the surgical pulsed laser beam in transverse directions, a Z scanner, to Z scan the XY scanned surgical laser beam along an optical axis, one or more auxiliary optical unit, generating auxiliary light, and an objective, to provide a shared optical pathway for the XYZ scanned surgical laser beam and the auxiliary light through an objective lens group into a surgical target region, wherein the lenses of the objective lens group do not move relative to each other, and the objective has no dynamic Z scanning function.

FIELD OF INVENTION

This invention relates to a system for surgery of the anterior segmentof the eye with a femtosecond laser, more particularly to embodimentsminimizing optical distortions of the laser beam while scanning andfocusing the laser beam into the eye.

BACKGROUND

This application describes examples and embodiments of techniques andsystems for laser surgery within the anterior segment of the eye thecrystalline lens via photodisruption caused by laser pulses. Variouslens surgical procedures for removal of the crystalline lens utilizevarious techniques to break up the lens into small fragments that can beremoved from the eye through small incisions. These procedures usemanual instruments, ultrasound, heated fluids or lasers and tend to havesignificant drawbacks, including the need to enter the eye with probesin order to accomplish the fragmentation, and the limited precisionassociated with such lens fragmentation techniques.

Photodisruptive laser technology can deliver laser pulses into the lensto optically fragment the lens without insertion of a probe and thus canoffer the potential for improved lens removal. Laser-inducedphotodisruption has been widely used in laser ophthalmic surgery andNd:YAG lasers have been frequently used as the laser sources, includinglens fragmentation via laser induced photodisruption. Some existingsystems utilize nanosecond lasers with pulse energies of several mJ (E.H. Ryan et al. American Journal of Opthalmology 104: 382-386, October1987; R. R. Kruger et al. Opthalmology 108: 2122-2129, 2001), andpicosecond lasers with several tens of μJ (A. Gwon et al. J. CataractRefract Surg. 21, 282-286, 1995). These relatively long pulses depositrelatively large amounts of energy into the surgical spots, resulting inconsiderable limitations on the precision and control of the procedure,while creating a relatively high level of risk of unwanted outcomes.

In parallel, in the related field of cornea surgery it was recognizedthat shorter pulse durations and better focusing can be achieved byusing pulses of duration of hundreds of femtoseconds instead of thenanosecond and picosecond pulses. Femtosecond pulses deposit much lessenergy per pulse, significantly increasing the precision and the safetyof the procedure.

Presently several companies commercialize femtosecond laser technologyfor ophthalmic procedures on the cornea, such as LASIK flaps and cornealtransplants. These companies include Intralase Corp./Advanced MedicalOptics, USA, 20/10 Perfect Vision Optische Geräte GmbH, Germany, CarlZeiss Meditec, Inc. Germany, and Ziemer Ophthalmic Systems AG,Switzerland.

However, these systems are designed according to the requirements of thecornea surgery. Crucially, the depth range of the laser focus istypically less than about 1 mm, the thickness of the cornea. As such,these designs do not offer solutions for the considerable challenges ofperforming surgery on the lens of the eye.

SUMMARY

Briefly and generally, a laser system for ophthalmic surgery includes alaser source to produce a surgical pulsed laser beam, an XY scanner toXY scan the surgical pulsed laser beam in transverse directions, a Zscanner, to Z scan the XY scanned surgical laser beam along an opticalaxis, one or more auxiliary optical unit, generating auxiliary light,and an objective, to provide a shared optical pathway for the XYZscanned surgical laser beam and the auxiliary light through an objectivelens group into a surgical target region, wherein the lenses of theobjective lens group do not move relative to each other, and theobjective has no dynamic Z scanning function.

In implementations the objective is configured to control at least oneof a spherical aberration, coma, and higher order aberrations of thesurgical pulsed laser beam.

In implementations the auxiliary optical unit comprises an opticalcoherence tomography imaging system. In implementations the auxiliaryoptical unit comprises an illumination light. In implementations theauxiliary optical unit comprises a visual observational block.

In implementations the objective is configured to focus the XYZ scannedlaser beam and the auxiliary light onto the surgical target region in arange of wavelengths encompassing the wavelength of the XYZ scannedlaser beam and the auxiliary light.

In implementations the range of wavelength includes the range of 0.4microns to 1.1 microns.

In implementations a mass of the objective is less than one of 400grams, 750 grams, 1,300 grams and 3,300 grams.

In implementations the objective includes a first lens group to receivethe XYZ scanned laser beam from the Z scanner and a second lens group toreceive a laser beam from the first lens group, the second lens groupincluding a first lens with an index of refraction in the range of 1.54to 1.72, an entry surface with a curvature in the range of 37.9 to 65l/m and an exit surface with a curvature in the range of −15.4 to 5.2l/m, a second lens, separated from the first lens by a distance in therange of 0 to 6.5 mm, with an index of refraction in the range of 1.56to 1.85, an entry surface with a curvature in the range of −55.1 to−21.8 l/m and an exit surface with a curvature in the range of 11.4 to26.8 l/m, wherein the second lens is configured to output the laser beamfrom the objective onto a patient interface.

In implementations a laser system for ophthalmic surgery includes alaser source to produce a pulsed laser beam, an XY scanner to scan thepulsed laser beam in transverse directions, a Z scanner, to scan a focalspot of the pulsed laser beam along an optical axis, and an objective,to focus the scanned pulsed laser beam onto a focal spot in a targetregion, having an internal entrance pivot point.

In implementations a mass of the objective is less than one of 400grams, 750 grams, 1,350 grams and 3,300 grams.

In implementations an effective focal length of the objective is lessthan 70 mm. In implementations a distance from the objective to apatient interface is less than 20 mm.

In implementations a curvature of a focal plane of the laser system islarger than 20 l/m.

In implementations the objective includes a first lens group to receivethe surgical pulsed laser beam from the Z scanner, and a second lensgroup, to receive the surgical pulsed laser beam from the first lensgroup, the second lens group including a first lens with an index ofrefraction in the range of 1.54 to 1.72, an entry surface with acurvature in the range of 37.9 to 65 l/m and an exit surface with acurvature in the range of −15.4 to 5.2 l/m, a second lens, separatedfrom the first lens by a distance in the range of 0 to 6.5 mm, with anindex of refraction in the range of 1.56 to 1.85, an entry surface witha curvature in the range of −55.1 to −21.8 l/m and an exit surface witha curvature in the range of 11.4 to 26.8 l/m, and the second lensoutputs the surgical pulsed laser beam from the objective onto a patientinterface.

In implementations a laser system for ophthalmic surgery includes alaser engine to generate a pulsed laser beam, an XY scanner to scan thepulsed laser beam in XY transverse directions, a Z scanner, to scan afocal spot of the pulsed laser beam along a Z axis, and an objective,having a mass of less than 3,300 grams.

In implementations a mass of the objective is less than 1,350 grams. Inimplementations a mass of the objective is less than 750 grams. Inimplementations a mass of the objective is less than 400 grams.

In implementations the mass of the objective is one of an optical massand a total mass.

In implementations the objective does not scan a Z focal depth of thefocal spot.

In implementations the objective has an entrance pivot point inside theobjective.

BRIEF DESCRIPTION OF FIGURES

FIG. 1 illustrates a surgical laser delivery system 1.

FIG. 2 illustrates a Gaussian wavefront G and an aberrated wavefront W.

FIGS. 3A-B illustrate rays at an optimal and a scanned focal plane.

FIG. 3C illustrates a definition of the focal spot radius.

FIG. 4 illustrates a relation between a Strehl ratio S and an RMSwavefront error ω.

FIG. 5 illustrates reference points for ophthalmic surgery.

FIGS. 6A-B illustrate conceptually the operation of precompensator 200.

FIGS. 7A-B illustrate various uses of an efficient Z scanningfunctionality.

FIGS. 8A-D illustrate implementations of the precompensator 200.

FIG. 9 illustrates an implementation of the laser delivery system 1 withtwo Z Scanners.

FIG. 10 illustrates a table of configurations containing 0, 1, or 2 Zdepth Scanner and 0, 1, or 2 NA modifiers.

FIGS. 11A-C illustrate an XY Scanner with 2, 3, and 4 scanning mirrors.

FIGS. 12A-D illustrate an aberration as a function of a numericalaperture and the corresponding optical numerical aperture NA_(opt)(z) asa function of the Z focal depth.

FIGS. 13A-B illustrate two settings of the First Beam Expander block 400and the Movable Beam Expander block 500.

FIG. 14 illustrates the intermediate focal plane of the Z Scanner 450.

FIG. 15 illustrates an implementation of the Objective 700.

FIG. 16 illustrates a curved focal plane in the target region.

FIG. 17 illustrates a nomogram of the XY Scanner inclination angle.

FIG. 18 illustrates a nomogram of the Movable Beam Expander position.

FIG. 19 illustrates steps of a computational control method.

DETAILED DESCRIPTION

Some embodiments of the present invention include systems for surgery inthe lens of the eye, utilizing femtosecond laser pulses. Some integratedembodiments are also capable of performing both corneal and lenssurgical procedures. Performing ophthalmic surgery in the lens of theeye is associated with qualitatively different requirements than cornealprocedures.

The key differences between the presently described lens surgical lasersystem and corneal systems include:

1. Femtosecond laser pulses are to be generated reliably. Highrepetition rate femtosecond pulses allow the use of a much smallerenergy per pulse, providing much higher control and precision for theoperator of the system. However, generating femtosecond pulses reliablyis a considerably greater challenge than nanosecond or picosend pulses,used by some existing systems.

2. The surgical laser beam is refracted considerably when propagatingthrough up to 5 millimeters of refractive medium, including the corneaand the anterior aqueous chamber just to reach the surgical target, thelens. In contrast, the laser beam used for corneal surgery is focused ata depth of a fraction of a millimeter, and is thus essentially notrefracted as it enters the cornea from the surgical system.

3. The surgical laser delivery system is configured to scan the entiresurgical region, for example from the front/anterior of the lens at atypical depth of 5 mm to the back/posterior of the lens at a typicaldepth of 10 mm. This 5 mm or more depth-scanning range, or “Z scanningrange”, is considerably more extensive than the 1 mm depth-scanningrange used for surgery on the cornea. Typically, the surgical optics,especially the here-used high numerical aperture optics, is optimized tofocus a laser beam to a specific operating depth. During cornealprocedures the 1 mm depth-scanning causes only moderate departure fromthe optimized operating depth. In contrast, during the scan from 5 to 10mm during lens surgery, the system is driven far from a fixed optimizedoperating depth. Therefore, the lens-surgical laser delivery systememploys a much-refined adaptive optics to be able to scan the extensivedepth-scanning range required by lens surgery.

4. Some embodiments are integrated in the sense that they are configuredto perform surgery on both the cornea and the lens. In these integratedembodiments the depth-scanning range can be up to 10 mm instead of 5 mm,posing even harder challenges.

5. During corneal surgical procedures, such as the many variants ofLASIK, the laser beam is scanned perpendicular to the optical axis (“inthe XY plane”). In typical procedures the XY scanning range covers onlythe central portion of the cornea with a diameter of 10 mm. However, inintegrated surgical systems additional cuts may be formed as well. Onetype of cuts is the entry cuts, providing access to the inside of theeye for aspiration needles and conventional surgical tools. Another typeof cuts is the limbal relaxing incisions (LRIs), which involve making apair of incisions at the corneal limbus just anterior to the vasculararcade. By adjusting the length, depth, and location of these arcuateincisions, one can induce changes in the corneal astigmatism. Entry cutsand LRIs can be placed at the periphery of the cornea, typically with adiameter of 12 mm. While increasing the XY scanning diameter from 10 mmto 12 mm diameter is only a 20% increase compared to the regulardiameter of LASIK flaps, it is a significant challenge to keep off-axisaberrations of the laser delivery system under control at suchdiameters, since off-axis aberrations grow proportional to higher powersof the field diameter at the focal plane.

6. Lens laser surgical procedures may require guidance fromsophisticated imaging systems. In some imaging systems limbal bloodvessels are identified to serve as reference marks on the eye, tocalibrate the cyclo-rotational alignment of the eye during the time ofsurgery, in some cases relative to the reference coordinates identifiedduring preoperative diagnosis of the eye. Blood vessels chosen on theperiphery of the surgical area can be the most undisturbed by thesurgery and thus the most reliable. Imaging systems directed to suchperipheral blood vessels, however, require the imaging optics to imagean area with a radius larger than 10 mm, such as 12 mm.

7. The laser beam develops various aberrations while propagating alongthe optical path within the eye. Laser delivery systems can improveprecision by compensating for these aberrations. An additional aspect ofthese aberrations is that they depend on the frequency of the light, afact referenced as “chromatic aberration”. Compensating these frequencydependent aberrations increases the challenge on the system. Thedifficulty of compensating these chromatic aberrations increases withthe bandwidth of the laser beam. a laser system. It is recalled that thespectral bandwidth of a beam is inversely proportional to the pulselength. Accordingly, the bandwidth for femtosecond pulses is oftengreater than that of picosecond pulses by an order of magnitude or more,necessitating a much better chromatic compensation in femtosecond lasersystems.

8. Surgical procedures using high repetition rate femtosecond lasersurgical systems require high precision in positioning each pulse bothin an absolute sense with respect to target locations in the targettissue and in a relative sense with respect to preceding pulses. Forexample, the laser system may be required to redirect the beam by only afew microns within the time between pulses, which can be of the order ofmicroseconds. Because the time between two subsequent pulses is shortand the precision requirement for the pulse placement is high, manualtargeting as used in existing low repetition rate lens surgical systemsis no longer adequate or feasible.

9. The laser delivery system is configured to deliver the femtoscondlaser pulses into the entire surgical volume of lens of the eye, througha refractive medium, with their temporal, spectral and spatial integritypreserved.

10. To ensure that only tissue in the surgical region receives a laserbeam with high enough energy densities to cause surgical effects, suchas tissue ablation, the laser delivery system has an unusually highnumerical aperture (NA). This high NA results in small spot sizes andprovides necessary control and precision for the surgical procedure.Typical ranges for the numerical aperture can include NA values largerthan 0.3, resulting in spot sizes of 3 microns or less.

11. Given the complexity of the optical path of the laser for lenssurgery, the laser delivery system achieves high precision and controlby including a high performance computer-managed imaging system, whereascorneal surgical systems can achieve satisfactory control without suchimaging systems, or with a low level of imaging. Notably, surgical andimaging functions of the system, as well as the customary observationalbeams generally all operate in different spectral bands. As an example,surgical lasers may operate at wavelengths in the band of 1.0-1.1micron, observational beams in the visible band of 0.4-0.7 micron, andimaging beams in the band of 0.8-0.9 micron. Combining beam paths incommon, or shared, optical components places demanding chromaticrequirements on the optics of the laser surgical system.

The differences 1-11 illustrate through several examples that ophthalmiclaser surgery (i) on the lens (ii) with femtosecond pulses introducesrequirements which are qualitatively different from those of cornealsurgery and even from lens surgery, using only nanosecond or picosecondlaser pulses.

FIG. 1 illustrates a laser delivery system 1. Before describing it indetail, we mention that some embodiments combine the laser deliverysystem of FIG. 1 with an imaging or an observational system. In somecorneal procedures, such as in LASIK treatments, eye trackers establishpositional references of the eye by visual clues such an identificationof the center of the iris by imaging and image processing algorithms,typically on the surface of the eye. However, existing eye trackersrecognize and analyze features in a two-dimensional space, lacking depthinformation, since the surgical procedures are performed on the cornea,the outermost layer of the eye. Often, the cornea is even flattened tomake the surface truly two dimensional.

The situation is quite different when focusing a laser beam in the lens,deep inside the eye. The crystalline lens can change its position,shape, thickness and diameter during accommodation, not only betweenprior measurement and surgery but also during surgery. Attaching the eyeto the surgical instrument by mechanical means can also change the shapeof the eye in an ill-defined manner. Such attaching devices can includefixating the eye with a suction ring, or aplanating the eye with a flator curved lens. Further, the movement of the patient during surgery canintroduce additional changes. These changes can add up to as much as afew millimeters of displacement of visual clues within the eye.Therefore, mechanically referencing and fixating the surface of the eyesuch as the anterior surface of the cornea or limbus are unsatisfactorywhen performing precision laser surgery on the lens or other internalportions of the eye.

To address this problem, laser delivery system 1 can be combined with animaging system, as described in co-pending application serial numberU.S. patent application Ser. No. 12/205,844 to R. M. Kurtz, F. Raksi andM. Karavitis, which is hereby incorporated by reference in its entirety.The imaging system is configured to image portions of a surgical regionto establish three dimensional positional references based on theinternal features of the eye. These images can be created before thesurgery and updated in parallel with the surgical procedure to accountfor individual variations and changes. The images can be used to directthe laser beam safely to the desired location with high precision andcontrol.

In some implementations, the imaging system can be an Optical CoherenceTomography (OCT) system. The imaging beam of the imaging system can havea separate imaging optical path, or an optical path partially or fullyshared with the surgical beam. Imaging systems with a partially or fullyshared optical path reduce the cost and simplify the calibration of theimaging and surgical systems. The imaging system can also use the sameor a different light source as the laser of the laser delivery system 1.The imaging system can also have its own beam scanning subsystems, orcan make use of the scanning subsystems of the laser delivery system 1.Several different architectures of such OCT systems are described in thereferred co-pending application.

The laser delivery system 1 can be also implemented in combination witha visual observation optics. The observation optics can help theoperator of the surgical laser to observe the effects of the surgicallaser beam and control the beam in response to the observations.

Finally, in some implementations, which use an infrared and thusinvisible surgical laser beam, an additional tracking laser may beemployed operating at visible frequencies. The visible tracking lasermay be implemented to track the path of the infrared surgical laser. Thetracking laser may be operated at a low enough energy not to cause anydisruption of the target tissue. The observation optics may beconfigured to direct the tracking laser, reflected from the targettissue, to the operator of the laser delivery system 1.

In FIG. 1, the beams associated with the imaging system and the visualobservation optics can be coupled into the laser delivery system 1 e.g.through a beam splitter/dichroic mirror 600. The present applicationwill not discuss extensively the various combinations of the laserdelivery system 1 with the imaging, observational and tracking systems.The large number of such combinations, extensively discussed in theincorporated U.S. patent application Ser. No. 12/205,844, are all withinthe overall scope of the present application.

FIG. 1 illustrates a laser delivery system 1, which includes a LaserEngine 100, a Precompensator 200, an XY Scanner 300, a First BeamExpander block 400, a Movable Beam Expander block 500, a BeamSplitter/dichroic mirror 600, an Objective 700 and a Patient Interface800, wherein the First Beam Expander block 400 and the Movable BeamExpander block 500 will be jointly referred to as Z Scanner 450.

In many implementations below the convention is used that the Zdirection is the direction essentially along the optical path of thelaser beam, or along the optical axis of the optical element. Thedirections transverse to the Z direction are referred to as XYdirections. The term transverse is used in a broader sense to includethat in some implementations the transverse and Z directions may not bestrictly perpendicular to each other. In some implementations thetransverse directions can be better described in terms of radialcoordinates. Thus the terms transverse, XY, or radial directions denoteanalogous directions in the described implementations, all approximately(but necessarily precisely) perpendicular to the Z direction.

1. Laser Engine 100

The laser engine 100 can include a laser to emit laser pulses withpredetermined laser parameters. These laser parameters may include pulseduration in the 1 femtosecond to 100 picosecond range, or within the 10femtosecond to 10 picosecond range, or in some embodiments the 100femtosecond to 1 picosecond range. The laser pulses can have an energyper pulse in the 0.1 microJoule to 1000 microJoule range, in otherembodiments in the 1 microJoule to 100 microJoule range. The pulses canhave a repeat frequency in the 10 kHz to 100 MHz range, in otherembodiments in the 100 kHz to 1 MHz range. Other embodiments may havelaser parameters which fall within a combination of these range limits,such as a range of pulse duration of 1-1000 femtosecond. The laserparameters for a particular procedure can be selected within these wideranges e.g. during a pre-operational procedure, or based on acalculation which is based on certain data of the patient, such ashis/her age.

Examples of the laser engine 100 can include Nd:glass and Nd:Yag lasers,and other lasers of a wide variety. The operating wavelength of thelaser engine can be in the infrared or in the visible range. In someembodiments the operating wavelength can be in the 700 nm-2 micronrange. In some cases the operating wavelength can be in the 1.0-1.1micron range, e.g. in infrared lasers based on Yb or Nd.

In some implementations the laser parameters of the laser pulses may beadjustable and variable. The laser parameters may be adjustable with ashort switch time, thus enabling the operator of the surgical laserdelivery system 1 to change laser parameters during a complex surgery.Such a change of parameters can be initiated in response to a reading bya sensing or imaging subsystem of the laser delivery system 1.

Other parameter changes can be performed as part of a multi-stepprocedure during which the laser delivery system may be first used for afirst surgical procedure, followed by a second, different surgicalprocedure. Examples include first performing one or more surgical stepsin a region of a lens of an eye, such as a capsulotomy step, followed bya second surgical procedure in a corneal region of the eye. Theseprocedures can be performed in various sequences.

High repetition rate pulsed lasers operating at a pulse repetition rateof tens to hundreds of thousands of shots per second or higher withrelatively low energy per pulse can be used for surgical applications toachieve certain advantages. Such lasers use relatively low energy perpulse to localize the tissue effect caused by the laser-inducedphotodisruption. In some implementations, for example, the extent of thedisrupted tissue can be limited to a few microns or a few tens ofmicrons. This localized tissue effect can improve the precision of thelaser surgery and can be desirable in certain surgical procedures. Invarious implementations of such surgeries, many hundreds, thousands ormillions of pulses can be delivered to a sequence of spots which arecontiguous, nearly contiguous, or are separated by controlled distances.These implementations can achieve certain desired surgical effects, suchas tissue incisions, separations or fragmentation.

The parameters of the pulses and the scan pattern can be selected byvarious methods. For example, they can be based on a preoperativemeasurement of the optical or structural properties of the lens. Thelaser energy and the spot separation can also be selected based on apreoperative measurement of optical or structural properties of the lensor on an age-dependent algorithm.

2. Precompensator 200

FIG. 2 illustrates that the wavefront of the laser beam can deviate froman ideal behavior in several different ways and for several differentreasons. A large group of these deviations are called aberrations.Aberrations (and the other wavefront distortions) displace real imagepoints from the ideal paraxial Gaussian image points. FIG. 2 illustrateswavefronts of light exiting through an exit pupil ExP. The undistortedspherical wavefront G emanates from the pupil and converges to a pointP1 at the center of curvature of the wavefront G. G is also called theGaussian reference sphere. An aberrated wavefront W deviates from G andconverges to a different point P2. The aberration ΔW of the aberratedwavefront W at point Q1 can be characterized by the optical length ofthe pathway relative to the undistorted reference sphere G: ΔW=n_(i)Q1Q2 , where n_(i) is the refractive index of the medium in the imagespace and Q1Q2 is the distance of points Q1 and Q2.

In general, the aberration ΔW depends on the coordinates both at theexit pupil as well as at the focal plane. Therefore, this aberration ΔWcan be also thought of as a correlation function: it represents that theset of points whose image converges to P2, removed from P1 on theoptical axis by r′, are located on a surface W, which deviates from thereference sphere G by an amount of ΔW at the radial distance r at theExit pupil ExP. For a rotationally symmetrical system, ΔW can be writtenin terms of a double power series expansion in r and r′ as:

$\begin{matrix}{{\Delta \; {W\left( {{r^{\prime};r},\Theta} \right)}} = {\sum\limits_{l = 0}^{\infty}{\sum\limits_{n = 1}^{\infty}{\sum\limits_{m = 0}^{\infty}{{{}_{{2l} + m}^{}{}_{}^{}}r^{{\prime \; 2l} + m}r^{n}\cos^{m}{\Theta.}}}}}} & (1)\end{matrix}$

Here r′ is the radial coordinate of the image point P2 in the focalplane and r is the radial coordinate of point Q1 at the pupil. Theangular dependence is represented by Θ, the spherical angle. n=2p+m is apositive integer and _(2l+m)a_(nm) are the expansion coefficients of theaberrated wavefront W. For reference, see e.g.: Optical Imaging andAberrations, Part I. Ray Geometrical Optics by Virendra N. Mahajan, SPIEOptical Engineering Press. The order i of an aberration term is given byi=2l+m+n.

The terms up to i=4 are related to the primary aberrations: spherical,coma, astigmatism, field curvature and distortion. The actual relationsbetween these primary aberrations and the _(2l+m)a_(nm) aberrationcoefficients are documented in the literature. For a system imaging apoint object, the explicit dependence of the aberration terms on theimage radius r′ can be suppressed by introducing the dimensionlessvariable ρ=r/a, where a is a transverse linear extent of the exit pupil,such as its radius:

$\begin{matrix}{{{\Delta \; {W\left( {\rho,\Theta} \right)}} = {\sum\limits_{n = 1}^{\infty}{\sum\limits_{m = 0}^{\infty}{a_{nm}\rho^{n}\cos^{m}\Theta}}}},} & (2)\end{matrix}$

where

$\begin{matrix}{a_{nm} = {a^{n}{\sum\limits_{l = 0}^{\infty}{{{}_{{2l} + m}^{}{}_{}^{}}{r^{{\prime \; 2l} + m}.}}}}} & (3)\end{matrix}$

A benefit of this notation is that the aberration coefficients a_(nm)all have the dimension of length and represent the maximum value of thecorresponding aberration at the exit pupil. In this notation, forexample, the spherical aberration is characterized by the aberrationcoefficient a₄₀.

While the description of aberration in terms of the aberrationcoefficients a_(nm) is mathematically well defined, it is not always theexperimentally most accessible approach. Therefore, three alternativeaberration measures are described next.

In the same vein of experimental accessibility and testability, it isnoted that the behavior of a beam in a biological tissue, such as theeye, may not be the easiest to measure. Helpfully, studies indicate thatrays in the eye may behave very analogously to rays in salty water withphysiologically appropriate salt concentration, where they can bequantitatively measured and described. Therefore, throughout theapplication when the laser delivery system's behavior in the eye isdescribed, it is understood that this description refers to behavioreither in the described eye tissue, or in corresponding salty water.

FIGS. 3A-C illustrate a second measure of aberrations. The laserdelivery system 1, which was configured to focus a beam at a focal plane210 at depth A, can cause a spherical aberration if it is operated tofocus the beam at an operating focal plane 211 at depth B instead. Sucha situation can occur, for example, during a three dimensional scanningprocedure, when the focal point of the laser beam is moved from focalplane 210 to focal plane 211.

FIG. 3A illustrates the case when the laser delivery system 1 focusesthe rays to their optimal focal plane 210. The rays pass through a spotat the optimal focal plane 210 (a “focal spot”) of very narrow radialextent, or radius, r_(f)(A). This radial extent r_(f)(A) can be greaterthan zero for a variety of reasons, such as the diffraction of the lightbeam. The radius of the focal spot can be defined in more than one ways.A common definition of r_(f)(A) is the minimal radius of the light spoton a screen as the screen's position is varied along the axial, or Z,direction. This Z depth is often called the “point of least confusion”.This definition is further refined in relation to FIG. 3C.

FIG. 3B illustrates the case when the laser delivery system 1 scans thefocus by some distance, such as a few millimeters, off the optimal focalplane 210, to an operating focal plane 211. Visibly, the rays passthrough a focal spot of a radius r_(f)(B) larger than r_(f)(A), causinga spherical aberration. Mathematical formulae of various accuracy havebeen developed connecting the aberration coefficients a_(nm) and thefocal spot radius r_(f). In some cases, the focal spot radius r_(f) isan experimentally more accessible measure to quantify the aberrationsthan the a_(mn) aberration coefficients.

FIG. 3C illustrates a more quantitative definition of the focal spotradius r_(f). FIG. 3C illustrates the energy contained in a spot ofradius r, measured from a centroid of the beam. A widely accepteddefinition of the focal spot radius r_(f) is the radius, within which50% of the beam's energy is contained. The curve labeled “A” shows thatin a diffraction limited beam, when the beam is focused to its optimalfocal plane 210, as in FIG. 3A, 50% percent of the beam's energy can becontained, or enclosed, in a spot of radius r=0.8 micron, providing auseful definition of r_(f)(A).

Surgical procedures based on laser induced optical breakdown (LIOB) canhave higher precision and efficiency and smaller undesirable effects ifthe laser beam's energy is deposited in a well or sharply defined focalspot. LIOB is a highly nonlinear process with an intensity (plasma-)threshold: typically, tissue exposed to a beam with intensity higherthan the plasma threshold turns into plasma, whereas tissue exposed to abeam with intensity below the plasma threshold does not undergo theplasma transition. Therefore, a broadening of the focal spot byaberration reduces the fraction of the beam which achieves intensity atthe focal plane higher than the plasma threshold and increases thefraction of the beam whose intensity remains below the threshold. Thislatter fraction of the beam is not absorbed effectively by the targettissue and continues to propagate through the eye tissue, in most casesto the retina, potentially causing undesirable retinal exposure.

For surgical procedures aimed at correcting the cornea, the focal planeis typically scanned, or shifted, in the Z direction (along the opticalaxis) only by about 0.6 mm from its optimal or nominal depth, since thethickness of the cornea is essentially 0.6 mm, in rare case thicker butstill does not exceed 1 mm. The curve labeled “B” illustrates that whenthe focal plane of a beam is shifted from its optimal focal plane 210 by1 mm (an upper estimate for corneal procedures) to the operating focalplane 211, 50% of the beam's energy is contained within the focal spotradius of r_(f)(B)=1.8 micron. While this shift introduces anaberration, but its measure is limited. Correspondingly, some of theexisting corneal laser systems do not compensate this aberration at all,while others introduce only some limited level of compensation.

Besides the aberration coefficients a_(mn) and the focal spot radiusr_(f), a third measure of aberrations is the so-called Strehl ratio S.The Strehl ratio S of a system can be defined referring to a beam whichemanates from a point source, as a peak intensity of the beam at thefocal plane of the system divided by the theoretical maximum peakintensity of an equivalent perfect imaging system, which works at thediffraction limit. Equivalent definitions are also known in theliterature and are within the scope of the definition of the Strehlratio S.

Corresponding to this definition, the smaller the value of S, the biggerthe aberration. An unaberrated beam has S=1 and conventionally, whenS>0.8, the imaging system is said to be diffraction limited.

A fourth definition of the aberrations is ω, a root-mean-square, or RMS,wavefront error which expresses the deviation ΔW of the aberratedwavefront W from the undistorted wavefront G of FIG. 2, averaged overthe entire wavefront at the Exit pupil ExP. ω is expressed in units ofthe wavelength of the beam, making it a dimensionless quantity.

FIG. 4 illustrates that for relatively small aberrations ω and S arerelated by the following empirical formula:

S≈e^(−(2πω)) ²   (4),

regardless of the type of aberration, where e is the base of naturallogarithm.

All four of the above measures of aberration are useful for diagnosingproblems and optimizing the design of the laser delivery system 1.Accordingly, below the general terminology “aberration measure” canrefer to any one of these measures, or their equivalents. Notably,increasing aberration is captured by an increase of the aberrationcoefficients a_(mn), focal spot radius r_(f) and RMS wavefront error ω,but by a decrease of the Strehl ratio S.

The relationship between these aberration measures is demonstrated byshowing the spherical aberration coefficient a₄₀ and the correspondingStrehl ratio S in a specific example. In the example, the surgical lasersystem focuses the laser beam in an ocular tissue at different depthsbelow its surface. The laser beam is diffraction limited, with a 1micrometer wavelength and NA=0.3 numerical aperture, and is focused atthe surface of the tissue at normal angle of incidence. The numbers ofthis example can be analogous to the effects of adding a plan parallelplate of thickness equal to the scanned depth near the focal plane ofthe system, and carrying out the calculation for salty water.

The surface of the tissue introduces aberrations in the beam,characterized by Equations (2) and (3). The spherical aberration,characterized by the aberration coefficient a₄₀, is zero at the surface,the Strehl ratio, by its very construction, is S=1.

LASIK surgeries typically form flaps in a depth of 0.1 mm. At thesedepths, the Strehl ratio S is reduced to about 0.996, only a smalldecrease. Even at 0.6 mm depth, approximately at the posterior surfaceof the cornea, S is about 0.85. While this is a non-negligible decreaseof peak intensity, but still can be compensated by adjusting the laserbeam intensity.

On the other hand, at 5 mm depth, characterizing the anterior surface ofthe crystalline lens in the eye, the Strehl ratio can decrease toS=0.054. At this depth and Strehl ratio, the beam intensity is reducedconsiderably below the plasma-threshold, and thus the beam is unable togenerate LIOB. This drastic loss of peak intensity cannot be compensatedby increasing the laser power without undesirable effects such as aserious over-exposure of the retina or excessively increased bubblesize.

Table 1 illustrates the spherical aberration a₄₀, corresponding to thejust-described Strehl ratios. Visibly, the spherical aberrationincreases approximately linearly with the tissue-depth, whereas theStrehl ratio S behaves in a non-linear manner:

TABLE 1 Depth in Spherical aberration Strehl tissue [mm] a₄₀ [micron]ratio S 0 0.00 1.000 0.1 −0.04 0.996 0.6 −0.24 0.856 5 −2.00 0.054 10−3.99 0.041

In surgical procedures aimed at performing lens lysis, capsulotomy, orother surgical procedures on the crystalline lens, the focal plane isoften scanned across the entire depth of the lens, which can be as muchas 5 mm. Moreover, in integrated cornea-lens systems, the total scanningdepth can extend from the cornea to the posterior surface of the lens,about 10 mm. The curve labeled “C” in FIG. 3C indicates that in suchcases the focal spot radius grow up to r_(f)(C)=18 microns, which valueis too large to even appear on the same plot as r_(f)(A) and r_(f)(B).In some embodiments, the optimal focal plane can be chosen to liehalfway in the depth-scanning range and the laser beam maybe scanned ina plus/minus 5 mm depth range. In this case r_(f)(C) can be reduced to10 microns.

These large r_(f)(C) values translate to a great amount of aberration inthe other three aberration measures a₄₀, S and ω. Clearly, in contrastto the corneal procedures which scan only a few tenth of a millimeter,these large aberrations of lens surgery pose numerous challenges for thedesign of the laser delivery system 1 to compensate or manage theirundesirable consequences.

To address the problem of large aberration measures, associated withlens surgery, some embodiments include the Precompensator 200 toprecompensate the spherical aberration and improve the aberrationmeasures. These aberrations can be developed in the target tissue, oralong a portion of the optical pathway within the laser delivery system1, or along the entire optical pathway.

FIG. 5 illustrates (not to scale) that, since the aberration measuresr_(f)(C), a₄₀, S and ω depend on the focal spot's depth z and its radialdistance r from the optical axis, in what follows when it is describedthat an aberration measure assumes a value, this will refer to theaberration measure assuming the described value at some selectedreference points. A set of relevant reference points can be described bytheir cylindrical coordinates (z, r): P1=(0,0), P2=(2,6), P3=(5,0),P4=(8,0), P5=(8,3), all in millimeters. Since the main structures of theeye exhibit an approximate cylindrical symmetry, these P referencepoints can be located at any azimuth angle φ. Therefore, these P pointswill be referred to only by two of their three cylindrical coordinates,the azimuth angle φ being suppressed. P1 is a typical point for acentrally located corneal procedure, P2 is typical for peripheralcorneal procedures, P3 is related to the anterior region of the lens, P4is related to the posterior of the lens, and P5 is a peripheral lensreference point. Other reference points can be adopted to characterizethe aberrations of a laser delivery system as well. In some cases, anaberration measure can refer to the aberration measure averaged over theoperational wavefront, or illuminated area.

The aberration measures can be determined in several different ways. Awavefront of the laser beam can be tracked in a computer-aided design(CAD) process through a selected section of the optical pathway, such asa model of the target tissue, or a section of the laser delivery system1. Or, the aberration of the laser beam can be measured in an actuallaser delivery system, or a combination of these two procedures.

Accordingly, in some implementations the precompensation, introduced bythe Precompensator 200 may be selected by determining, calculating ormeasuring an aberration measure along a selected portion of the opticalpathway, which may include the target tissue itself and then determiningan amount of precompensation which is needed to compensate a preselectedportion of the determined/calculated/measured aberration.

The Precompensator 200 can correct, or precompensate, the sphericalaberration efficiently, because the spherical aberrations dominantlyaffect axial rays. Other types of aberrations, such as transverseaberrations, astigmatism and coma, affect non-zero angle rays as well asfield rays, including rays being offset from the optical axis. While thelaser beam, generated by the laser engine 100 is an essentially axialbeam, the various blocks in the optical pathway, most notably the XYScanner 300, transform this axial beam into a non-zero angle beam,having field rays.

Therefore, in designs where a precompensator is placed after the XYScanner 300, the field rays of the beam can develop several differentaberrations. This emergence of different aberrations poses great designchallenges because (i) the optimization of the beam may requirecompensating several of the aberrations, and (ii) the different types ofaberrations are not independent from each other. Thus, compensating onetype of aberration typically induces unwanted other types of aberration.

Therefore, in architectures where a compensator is placed after the XYscanner, the spherical aberrations are typically compensated only to alimited degree and at the expense of introducing other types of unwantedaberrations.

In contrast, embodiments of the present laser delivery system 1 can havethe Precompensator 200 before the XY Scanner 300. This design allows thePrecompensator 200 to precompensate a spherical aberration withoutintroducing other types of unwanted aberrations.

Some implementations can even exploit the above mentionedinterdependence of the on-axis and the off-axis aberrations byintroducing an on-axis precompensation by the Precompensator 200 toprecompensate an off-axis aberration, caused by a subsequent segment ofthe laser delivery system or the target tissue.

FIGS. 6A-B illustrate schematically an idealized operation of thePrecompensator 200.

FIG. 6A illustrates a laser delivery system 1 without a precompensator.In general, an optical pathway segment 301 can introduce some level ofspherical aberration. This is shown by an undistorted wavefront enteringthe optical pathway segment 301 and a wavefront with aberration leavingthe optical pathway segment 301. This segment can be any segment of theoptical pathway, such as a portion of the target tissue, or the entiretarget tissue, or a portion of the pathway within the laser deliverysystem 1.

FIG. 6B illustrates that the Precompensator 200 can introduce acompensating (or complementary) distortion of the wavefront. Thisprecompensated wavefront then enters the optical pathway segment 301,causing it to output a wavefront with reduced distortion, or evenwithout distortion.

Some existing systems do not have a dedicated compensator at all. Othersystems may compensate the spherical aberration only in a distributedmanner by the lenses of lens groups which have other functions as welland are positioned after the XY scanner. In these existing systems, theparameters of the lenses are chosen as a result of making compromisesbetween different functionalities, leading to limitations on theirperformance.

In contrast, embodiments of the laser delivery system 1 can have thededicated Precompensator 200 disposed before the XY Scanner 300. In someembodiments, the Precompensator 200 is the first optical unit, or lensgroup, which receives the laser beam from the laser engine 100. Sincebecause of its location the laser beam reaches the Precompensator 200without developing non-zero angle rays or field rays (which could becaused by the XY Scanner 300), these embodiments can achieve a highlevel of precompensation. The precompensation is also efficient becauseit is a primary function of the Precompensator 200 and thus designcompromises can be kept very limited, as opposed to existing systems,which compensate with lenses serving additional functions.

For these reasons, in such implementations it is possible to correct thespherical aberration to a high degree without affecting or introducingother types of aberrations.

It is known in the theory of aberrations, that the spherical aberrationof a compound lens system is approximately the sum of sphericalaberrations of individual components. Therefore, in some implementationsof the laser delivery system 1, an unwanted amount of sphericalaberration can be precompensated by designing the Precompensator 200 tointroduce an equal amount of aberration, but with the opposite sign.

As an example, when the depth of the focal spot inside the eye tissue ismoved by 5 mm off its optimal focal plane, the spherical aberration a₄₀(according to Table 1) is −2.0 micrometers. Accordingly, in someimplementations the Precompensator 200 can introduce an aberrationmeasure of a₄₀=+2.0 micrometers. In a first approximation thisprecompensation may essentially eliminate the spherical aberrationcaused by the 5 mm shift of the focal spot and correspondingly increasethe Strehl ratio from S=0.054 back to S=1. (This simple exampledisregarded other sources of aberrations.)

Some implementations below will be characterized by comparing theaberration measures of “non-precompensated” laser delivery systems 1,i.e. laser delivery systems where the Precompensator 200 has beenremoved, to “precompensated” laser delivery systems, i.e. systems wherethe Precompensator 200 has not been removed.

In some implementations, installing the Precompensator 200 can increasethe Strehl ratio from a value S<S(precomp) of the non-precompensatedlaser delivery system 1 to a value S>S(precomp) for the precompensatedlaser delivery system 1. In some implementations S(precomp) can be 0.6,0.7, 0.8 or 0.9, for example.

As stated above, this Strehl ratio S here and below can refer to any oneof the Strehl ratios S(P1), . . . S(P5) at the five reference pointsP1-P5 above, or to the Strehl ratio at some other predeterminedreference points, or to an average of the Strehl ratios over the fivereference points, or to an average over the operational wavefront.

Also, the Strehl ratio can refer to the entire laser delivery system 1,receiving the laser beam from Laser Engine 100, ending with theObjective 700 and forming the focal spot in an ophthalmic target tissue.In some other cases the term can refer to other targets, including air.In some implementations the term can refer to a subsystem of the laserdelivery system 1.

In some implementations, the addition of the Precompensator 200 to thenon-precompensated laser delivery system 1 can increase a Strehl ratiofrom a non-precompensated value below S=S(precomp) to a precompensatedvalue above S=S(precomp) for pulses having an associated bandwidth atleast an order of magnitude larger than the transform-limited bandwidthof laser pulses with a duration of a picosecond or longer. As above,S(precomp) can be 0.6, 0.7, 0.8, or 0.9, for example.

In some implementations the addition of the Precompensator 200 to thelaser delivery system 1 can increase a Strehl ratio from anon-precompensated value below S=S(precomp) to a precompensated valueabove S=S(precomp) over a range of wavelengths of 0.4 microns to 1.1microns. As above, S(precomp) can be 0.6, 0.7, 0.8, or 0.9, for example.

In some implementations the addition of the Precompensator 200 canincrease a system numerical aperture from a non-precompensated valuebelow NA=NA(precomp), corresponding to the laser delivery system 1without the Precompensator 200, to a precompensated value aboveNA=NA(precomp) with the Precompensator 200. In some implementations, thevalue of NA(precomp) can be 0.2, 0.25, 0.3 or 0.35, for example.

In some implementations adding the Precompensator 200 to a laserdelivery system 1 without one can decrease the focal spot radius r_(f)in a target tissue from a non-precompensated value above r_(f)(precomp)to a precompensated value below r_(f)(precomp), corresponding to thelaser delivery system 1 with the Precompensator 200. In someimplementations r_(f)(precomp) can be 2, 3 or 4 microns.

In some implementations, installing the Precompensator 200 can increasethe RMS wavefront error from a value ω>ω(precomp) of thenon-precompensated laser delivery system 1 to a value ω<ω(precomp) forthe precompensated laser delivery system 1. In some implementationsω(precomp) can be 0.06, 0.07, 0.08 or 0.09, all in units of thewavelength of the laser beam, for example.

In some implementations, installing the Precompensator 200 can increasethe spherical aberration coefficient from a value a₄₀>a₄₀(precomp) ofthe non-precompensated laser delivery system 1 to a valuea₄₀<a₄₀(precomp) for the precompensated laser delivery system 1. In someimplementations a₄₀(precomp) can be 2, 3, or 4 micrometers, for example.

In some implementations, installing the Precompensator 200 into anon-precompensated laser delivery system 1 can reduce at least one ofthe following aberration measures: the RMS wavefront error ω, thespherical aberration measure a₄₀ and the focal spot radius r_(f) from anon-precompensated value by at least a precompensation percentageP(precomp), or increase a Strehl ratio S by at least the precompensationpercentage P(precomp). In some implementations P(precomp) can be 10%, or20%, or 30%, or 40%, for example.

As described above, any one of these aberration measures can belong toany one of the reference points P1, . . . P5, or to some otherpredetermined reference points, or to an average of values at referencepoints, or can be an average over the wavefront.

In some embodiments, the Precompensator 200 can compensate non-sphericalaberrations, such as first, or higher order aberrations as well. In somecases it can perform precompensation of off-axis rays too.

In some implementations, the Precompensator 200 precompensates othertypes of aberrations, while not increasing the RMS wavefront error bymore than 0.075, or by keeping the Strehl ratio above S(precomp), havinga value of e.g. 0.8.

In some implementations the Precompensator 200 can increase the radiusof the beam rb exiting the Precompensator 200 to a value aboverb=rb(precomp), where rb(precomp) can be e.g. 5 mm or 8 mm.

Some of these functionalities can be reached by including one or moremovable lenses into the Precompensator 200. Position actuators can movethe movable lens or lenses, changing the distance between some of thelenses of the Precompensator 200.

In implementations with one movable lens, the movable lens of thePrecompensator 200 can move the focal plane or spot of the laserdelivery system 1 along the optical axis by 0.3-4.0 mm. In some otherimplementations, by 0.5-2.0 mm.

In some implementations, when at least one of the Strehl ratios S(low)at the above described five reference points P1, . . . P5 is belowS=S(movable) when the movable lens is in a median position, the movablelens can be moved to increase the Strehl ratio S(low) to a value aboveS=S(movable). S(movable) can be 0.6, 0.7, 0.8 or 0.9.

In some implementations the movable lens can be moved to vary the Strehlratio S in the range 0.6-0.9. In other implementation in the range0.70-0.85.

Since the Precompensator 200 is located before the XY Scanner 300 orother beam expanders, the beam radius is still small. Therefore, themovable lens can be small. And since the movable lens is small, theposition actuators can move it very fast, allowing for a very quickchanging of the focal depth. This feature speeds up the depth scanning,or Z scanning in these embodiments and can make the Z scanning speedcomparable to the typically faster XY scanning speed.

In some typical existing systems, the aberrations are compensateddominantly by optical means, such as lenses. The presently describedmovable lens Precompensator 200 can utilize the fast movable lens orlenses to carry out this function well. In particular, when the laserbeam is scanned with the XY Scanner 300, the movable lens or lenses canbe moved with a sufficiently high speed so that the aberrationsassociated with the XY scanning get compensated to a desired level.

FIG. 7A illustrates that this aspect can be useful when a transversesurgical cut 206 is performed essentially tracking the contact surfaceof a planar or curved patient interface 208. The speed of the smallmovable lens makes it possible that the Z scanning is performed at thespeed required by the XY scanning, forming the desired curved cut.

In some implementations a curvature, or radius, of the curved cut, orcurved target line can be smaller than 1 mm, 10 mm, and 100 mm.

FIG. 7B illustrates another useful aspect of a high Z scanning speed.The focal plane of most optical systems is somewhat curved. If it isdesired to create an essentially straight transversal cut, whichtherefore does not track the curvature of the focal plane, the focaldepth needs to be continuously re-adjusted, synchronously with the fasttransverse XY scanning to compensate for the curvature of the focalplane. For example, for radial cuts or planar cuts with a raster scanpattern the change of the radial, or XY coordinate, can be very fast. Inthese procedures a fast Z scanning speed can help forming the desiredstraight cut.

Finally, the high Z scanning speed can be also useful to perform somesurgical procedures fast, such as corneal procedures.

In some implementations, the movable lens Precompensator 200 can changethe depth of the focal spot of the laser delivery system with an axialspeed at least 5% of the maximum transversal scanning speed of the focalspot. In some implementations with an axial speed at least 10% of themaximum transversal scanning speed of the focal spot. In otherembodiments with an axial speed at least 20% of the maximum transversalscanning speed of the focal spot.

In some implementations, the movable lens Precompensator 200 can changethe Z coordinate of the focal spot by 0.5-1 millimeter in a Z scanningtime.

In some implementations this Z scanning time can be in the range of10-100 nanoseconds, 100 nanoseconds-1 millisecond, 1 millisecond-10milliseconds and 10 milliseconds-100 milliseconds.

In some implementations the movable lens of the lens group is movable ina Z moving range to reduce a first aberration measure by at least amovable percentage P(movable). Here the first aberration measure can bea spherical aberration coefficient a₄₀, an RMS wavefront error ω, and afocal spot radius r_(f), and the movable percentage P(movable) can be10%, 20%, 30% and 40%.

In some implementations the movable lens of the lens group is movable ina Z moving range to increase a Strehl ratio S by at least a movablepercentage P(movable), which can be 10%, 20%, 30% and 40%.

In some implementations, the movable lens Precompensator 200 is capableof changing a numerical aperture NA of the laser delivery system 1, a Zdepth of the focal spot, any one of the aberration measures and a beamdiameter essentially independently by moving the movable lens. In otherwords, moving the movable lens is capable of varying any one of thesefour characteristics of the laser delivery system 1 without changing theother two characteristics. These embodiments offer considerable controlfor the operator of the embodiment.

Some of the functions of the Precompensator 200 are sometimes referredto as beam conditioning or beam expanding. Correspondingly, in someexisting systems blocks with analogous functions are referred to as beamconditioner or beam expanders.

In some embodiments the Precompensator 200 includes just one lens toachieve the above functionalities.

In some embodiments the Precompensator 200 includes two to five lensesto achieve the above functionalities.

FIG. 8A illustrates a three lens embodiment of Precompensator 200,including lens 221, lens 222 and lens 223.

FIG. 8B illustrates a three lens embodiment of movable lensPrecompensator 200′, including lens 221′, movable lens 222′ and lens223′.

FIG. 8C illustrates a four lens embodiment of Precompensator 200″,including lenses 231-234.

FIG. 8D illustrates a four lens embodiment of movable lensPrecompensator 200′″, including lens 231′, movable lens 232′, lens 233′and lens 234′.

Tables 2-4 illustrate various three lens implementations of thePrecompensators 200 and 200′ of FIGS. 8A-B. Embodiments of thePrecompensator 200 can be implemented using thin lenses. Therefore, theycan be described in terms of refractive powers of the individual lensesand their distances from the next lens.

Table 2 illustrates a three fixed lens embodiment of Precompensator 200,also shown in FIG. 8A. In Table 2 column 1 shows the lens number, column2 the refractive power measured in diopters Di (i=1, 2, 3), and column 3the distance di (i=1, 2) between lenses i and i+1.

TABLE 2 for FIG. 8A Lens Refractive Distance to next number power [1/m]lens [mm] 221 D1 = (−3, −5) d1 = (60, 100) 222 D2 = (3, 5) d2 = (3, 9)223 D3 = (−3.5, −6)

Table 3 illustrates a possible implementation of Precompensator 200′with two movable lenses 222′ and 223′, as in FIG. 8B, showing lensspacings diA and diB in two configurations A and B in columns 3 and 4.The lens spacings di can vary continuously between diA and diB.

TABLE 3 for FIG. 8B Distance to next Distance to next Lens Refractivelens [mm], lens [mm], number power [1/m] Configuration A Configuration B221′ D1 = (−3, −5) d1 = (60, 100) d1B = (1.0, 9.0) 222′ D2 = (3, 5) d2 =(3, 9) d2B = (20, 40) 223′ D3 = (−3.5, −6)

Table 4 illustrates that in various implementations the above parametersDi and di can assume values in broad intervals, depending on a largenumber of design considerations, such as different beam sizes andavailable space. Some of the parameters of these implementations can beconnected to the embodiments of Tables 2-3 by scaling: the refractivepowers with a scaling factor a, and the distances with a correspondingscaling factor 1/a. Furthermore, the refractive powers can beadditionally modified by tolerance factors t1 trough t3 to allow fordifferences in tolerances and design implementations. These relationsare summarized in Table 4:

TABLE 4 for FIGS. 8A-B Lens Refractive Distance to next number power[1/m] lens [mm] 221 D1*a*t1 d1/a 222 D2*a*t2 d2/a 223 D3*a*t3

In some implementations the scaling factor a can be in a range of 0.3 to3, and the tolerance factors t1, t2, and t3 can be in a range of 0.8 to1.2.

Analogously, Table 5 illustrates various four lens implementations ofthe Precompensator 200″, wherein the lenses 231, 232, 233 and 234 arefixed, as shown in FIG. 8C.

TABLE 5 for FIG. 8C Lens Refractive Distance to next number power [1/m]lens [mm] 231 D1 = (−15, −20) d1 = (100, 130) 232 D2 = (−5, −8) d2 =(32, 41) 233 D3 = (−25, −35) d3 = (33, 45) 234 D4 = (7, 10)

Table 6 illustrates a four lens implementation of the Precompensator200′″ of FIG. 8D, with one movable lens 232′.

TABLE 6 for FIG. 8D Distance to next Distance to next Lens Refractivelens [mm], lens [mm], number power [1/m] Configuration A Configuration B231 D1 = (−15, −20) D1A = (100, 130) d1B = (120, 140) 232 D2 = (−5, −8)d2A = (32, 41) d2B = (20, 30) 233 D3 = (−25, −35) d3A = (33, 45) d3B =(31, 42) 234 D4 = (7, 10)

As in the three lens implementations, the parameters of the four lensPrecompensators 200″ and 200′″ can assume values in broad ranges.Parameters of some of these implementations again can be related to eachother by scaling factors a, 1/a, t1, t2, t3, and t4, respectively, inanalogy to Table 4. The scaling factor a can be in the range of 0.2 to 5and the tolerance factors t1, . . . t4 can be in a range of 0.7 to 1.3.

In other embodiments, other combinations and ranges are employed. Withinthese ranges, many embodiments of the laser delivery system 1 arepossible, as the system can be optimized for many differentfunctionalities resulting in different choices. Design compromises andoptimization constraints can lead to a large number of implementations,each with its own advantages. The large number of possibilities isillustrated by the ranges of parameters in the above Tables 2-6.

In a one movable lens implementation of the Precompensator 200′ themoving lens can change one of the laser system's characteristicsessentially independently. These parameters include the Z focal depth,the numerical aperture NA, any one of the aberration measures, and adiameter of the exit beam. For example, these implementations allow theoperator to change e.g. the numerical aperture of the laser deliverysystem 1, without changing e.g. the Z focal depth.

In some implementations the Precompensator 200 has two independentlymoving elements. Such implementations allow the operator toindependently control two characteristics of the laser beam, such ase.g. the beam diameter and the numerical aperture NA, while keeping theaberrations fixed.

FIG. 9 illustrates an embodiment of the laser delivery system 1′, wherea Z scanning functionality of various optical blocks is highlighted. Inparticular, the laser engine 100 generates a laser beam, which isreceived by a first Z Scanner 250. The first Z Scanner 250 receives thelaser beam from the laser engine 100 and scans a focal point of thelaser delivery system 1′ over a first Z interval along an optical axisof the laser delivery system 1′. The beam, outputted by the first ZScanner 250 is received by the XY Scanner 300, which scans the laserbeam in a direction essentially transverse to the optical axis of thelaser system. The outputted XY scanned laser beam is then received by asecond Z Scanner 450, which scans the focal point of the laser systemover a second Z interval along the optical axis of the laser system.

In some embodiments, the first Z Scanner 250 is configured so that thefirst Z interval is suitable for a corneal surgical procedure, and thesecond Z Scanner 450 is configured so that the second Z interval issuitable for an anterior segment surgical procedure.

In some embodiments, the first Z interval is within the range of 0.05-1mm and the second Z interval is within the range of 1-5 mm.

In some embodiments the first Z interval is within the range of 1-5 mmand the second Z interval is within the range of 5-10 mm.

In some embodiments the first Z Scanner 250 is configured to scan thefocal point over the first Z interval of 0.05 mm-1 mm in a first Zscanning time. The first Z scanning time can be in one of the ranges of10-100 nanoseconds, 100 nanoseconds-1 millisecond, 1 millisecond-10milliseconds, and 10 milliseconds-100 milliseconds.

In some embodiments the second Z Scanner 450 is configured to scan thefocal point over the second Z interval of 1 mm-5 mm in a second Zscanning time. The second Z scanning time can be in one of the ranges of10-100 milliseconds, and 100 milliseconds-1 second.

In some embodiments the first Z Scanner 250 is configured to change thenumerical aperture of the laser beam by more than 10%.

In some embodiments the second Z Scanner 450 is configured to change thenumerical aperture of the laser beam by more than 10%.

In some embodiments the first Z Scanner 250 is configured to change thenumerical aperture of the laser beam by more than 25%.

In some embodiments the second Z Scanner 450 is configured to change thenumerical aperture of the laser beam by more than 25%.

FIG. 10 shows a summary table of the many variations of the abovedescribed elements. As shown, some implementations can have 0 Z depthscanners, 1 Z depth scanner before the XY Scanner 300, 1 Z depth scannerafter the XY Scanner 300 and 2 Z depth scanners, one before and oneafter the XY Scanner 300.

Further, some implementations can have 0 NA controller, 1 NA controllerbefore the XY Scanner 300, 1 NA controller after the XY Scanner 300 and2 NA controllers, one before and one after the XY Scanner 300.

Here, the Z Scanners and NA controllers quite generally refer to asingle lens or a lens group, which can modify the Z depth and thenumerical aperture NA, respectively. In some cases these modifiers canbe activated, or controlled by a single electric actuator, which makesthe lenses of the modifier move synchronously to modify the NA or the Zdepth of the beam.

Both the Z Scanners and the NA controllers can be housed in the first ZScanner 250 and the second Z Scanner 450 of FIG. 9. In some cases thecorresponding optical elements are distinct, in other implementationsthe Z Scanner and the NA controller which are housed in the same ZScanner block 250 or 450, can share one or more lenses, movable lenses,or electric actuators.

As shown in FIG. 10, 0 Z scanners and one or two NA controllers operateat fixed Z depth, but can control NA during the XY scanning.

1 Z Scanner and 0 NA controller can perform the Z scanning.

1 Z Scanner and 1 or 2 NA controllers can perform, in addition to the Zscanning, a control of the NA.

2 Z Scanners can perform Z scanning at two speeds and also control theNA, when combined with 1 or 2 NA controllers.

Non-lens optical elements are also used in some implementations, such asvariable apertures and pupils.

In addition, most of the illustrated 16 combinations can be furtherconfigured to precompensate a selected aberration, such as the sphericalaberration.

FIG. 10 illustrates that the various system characteristics, such as theZ depth of the beam, its numerical aperture NA and its aberration,represented by its aberration measure such as the Strehl ratio S, can becontrolled or adjusted independently of each other. Such embodimentsoffer a great control and precision to the operator of laser deliverysystem 1.

In analogous embodiments, such double beam conditioning can be performedfor other pairings of beam characteristics. For example, similar tableswith 4×4=16 pairings can be created regarding an aberration controllerand a beam diameter controller. Here 0, 1, or 2 aberration controllerscan be paired in all possible combinations with 0, 1 or 2 beam diametercontrollers.

The list of beam characteristics includes: Z depth of the focal spot,the numerical aperture NA, the beam radius, and any aberration measure,such as the Strehl ratio S, the focal spot radius r_(f), the RMSwavefront error ω and the spherical aberration measure a₄₀.

3. XY Scanner 300

The XY Scanner 300 may receive the precompensated beam from thePrecompensator 200, either directly of indirectly, having passed throughsome intermediate optical elements. A function of the XY Scanner 300 maybe to scan the beam received from the Precompensator 200 in a directionessentially transverse to an optical axis of the laser delivery system1. In various embodiments, the “transverse” direction is not necessarilyperpendicular to the optical axis, and can include any direction whichmakes a substantial angle with the optical axis.

In some embodiments the XY Scanner 300 outputs a scanning laser beam,which, having propagated through the laser delivery system 1 and havingreached the surgical region, scans in a transverse direction from zeroto a maximum of an XY scanning range of 5-14 mm. In some implementationsmaximum of the XY scanning range is between 8 and 12 mm.

FIG. 11A illustrates that the XY Scanner 300 can include an X scannerand a Y scanner. In some existing designs the X and the Y scanner eachinclude one mirror: a single X scanning mirror 310 and a single Yscanning mirror 320. In such designs the beam deflected by the Xscanning mirror 310 hits the Y scanning mirror 320 at different pointsdepending on the orientation of the X scanning mirror 310. Inparticular, when the X scanning mirror 310 is in position 310 a, theincident beam 331 is reflected as beam 332 a, whereas when the Xscanning mirror is rotated into position 310 b, the incident beam isreflected as beam 332 b.

These two beams 332 a and 332 b hit the Y scanning mirror 320 indifferent positions and therefore even for a fixed Y scanning mirror 320in position 320 a they will give rise to two different reflected beams333 aa and 333 ba, respectively. Worse yet, when the Y scanning mirror320 itself is rotated from position 320 a to 320 b, the two incidentbeams 332 a and 332 b give rise to two additional reflected beams 333 aband 333 bb, all four beams 333 aa, 333 ab, 333 ba, and 333 bbpropagating in different directions.

The problem can be characterized in terms of the notion of a pivotpoint. One definition of a pivot point of a scanning optical element canbe as the point through which essentially all rays go through, havingexited from the optical scanning element. This notion is the analogue ofthe focal point of non-moving refractive elements, as applied for movingoptical elements, such as scanners.

Using this terminology, the above problem can be traced back in FIG. 11Ato the X scanner pivot point 315X being fixed on the X scanning mirror310 itself. The outputted scanned beam will appear for the subsequentoptical elements as having emanated from a single pivot point 315X onthe X scanning mirror 310, and thus propagating into a wide range ofangles. This divergence of the two mirror designs can lead to severaldifferent types of undesirable aberrations.

FIG. 11B illustrates an existing three mirror XY Scanner 300′, where theX scanner 310 includes two mirrors 311 and 312 to address this problem.For clarity, the mirrors are shown from the side. In this design, Xscanning mirrors 311 and 312 perform the X scanning function in acoordinated manner. As shown in FIG. 11B, as the first X scanning mirror311 changes its orientation from 311 a to 311 b, the second X scanningmirror 312 can be rotated in a coordinated manner from 312 a to 312 b.These coordinated scanning rotations make it possible that the deflectedbeams 332 a and 332 b in the two rotational states go through a pivotpoint 315X, which is lifted off the X scanning mirrors.

Since the X scanner pivot point 315X has been lifted from the X scanningmirror itself, its location can be adjusted. In the design of FIG. 11B,the X scanning mirrors are designed to place the pivot point 315Xessentially onto the Y scanning mirror 320. In such designs the problemof the X scanner 310 in FIG. 11A is essentially resolved and thecorresponding aberrations are much reduced.

However, even this design has a problem analogous to that of FIG. 11A,only in the context of the Y scanning mirror 320. In the design of FIG.11B, the Y scanner pivot point 315Y is still fixed to the Y scanningmirror.

The entrance pupil of an optical system is the image of the aperturestop when viewed from the front of the system. The exit pupil is theimage of the aperture stop in the image space. In an optical system withmultiple groups of lenses the locations of the entrance and exit pupilsare often carefully adjusted. In many designs, the exit pupil of onelens group matches the entrance pupil of the following lens group.

For the XY scanner 310 the pivot point can be regarded as the exitpupil. In some embodiments this exit pupil matches the entrance pupil ofthe following lens group, such as the Z Scanner 450. However, theentrance pupil of that lens group may be inside the physical boundariesof the lens group, where a scanner block cannot be placed. In that casea scanner block is desirable for which the pivot point is outside thephysical boundaries of the scanner block, at a location which can bearbitrarily chosen.

FIG. 11C illustrates a four mirror design to address this problem. Inthe XY Scanner 300″ the X scanner 310 again includes two X scanningmirrors 311 and 312. However, the Y scanner also includes two Y scanningmirrors, 321 and 322.

XY Scanner 300″ removes the Y scanner pivot point 315Y from the Yscanning mirror. Accordingly, XY Scanner 300″ can control the Y scanner,or output, pivot point 315Y to a predetermined location. An example isto move the Y scanning-output pivot point 315Y onto the entry pupil 340of a subsequent lens group. In some implementations the X pivot point315X can be also moved to the same location as well.

Other aspects of this design include that XY Scanner 300″ can controlessentially independently (i) an angle α between the outputted scannedbeam and an optical axis of the laser delivery system 1, and (ii) alocation where the scanning beam impacts the entrance pupil of thesubsequent optical element, characterized by a distance d from theoptical axis. Because of the approximate independence of these controls,the XY Scanner 300″ can provide a scanning beam with minimizedaberrations, as well as can control astigmatism and coma in theperipheral regions, including the peripheral regions of the surgicalregion.

Some implementations of XY Scanner 300′″ include only one X scanningmirror 310 and one Y scanning mirror 320, each of them of the “faststeering” type. An individual fast steering mirror is capable of angularmotion around two axes of rotation. A pair of these fast steeringmirrors can also control the beam angle and the beam position in theplane transversal to the optical axis.

In some implementations the XY Scanner 300′″ is configured to scan thelaser beam over an XY scanning range whose maximum is longer than 5millimeter and shorter than 15 millimeter at the focal plane of thelaser system.

In some implementations the X pivot point generated by the first andsecond XY fast steering mirrors and the Y pivot point generated by thefirst and second XY fast steering mirrors coincide.

4. Z Scanner 450

As described above, ophthalmic surgical systems are configured toperform anterior segment surgery, or lens surgery by having a designwhich allows scanning a focal point over an interval much larger thanthe scanned interval in corneal procedures. In some implementations theZ scanning is performed over a Z scanning path within the Z scanningrange of 5 mm to 10 mm, or 0 mm to 15 mm. (Throughout this application,the term “scanning within a range of x mm to y mm” refers to a scanningpath whose initial value is x mm or more and ending value is y mm orless, encompassing all scanning paths which do not extend across theentire scanning range.)

Here, it is recalled that the “X, Y, Z” assignments are meant throughoutthe implementations in a broad sense. Z typically denotes an opticalaxis, which can be close to a geometrical axis. But the Z directioninside a target tissue, such as the eye, may not be fully parallel tothe optical axis of the laser delivery system 1. Any compromise axisbetween these two can be also referred to as the Z direction. Also, theX, Y directions are not necessarily perpendicular to the Z axis. Theycan refer to any direction making a substantial angle with the Zdirection. Also, in some implementations, a radial coordinate system maybe more suitable to describe the scanning of the laser delivery system1. In those implementations, the XY scanning refers to any scanning notparallel to the Z axis, parametrized by suitable radial coordinates.

FIG. 1 illustrates that some implementations of the laser deliverysystem 1 achieve these challenging large Z scanning ranges by includingthe First Beam Expander block 400 and the Movable Beam Expander block500 in the Z Scanner 450. In various implementations, the First BeamExpander block 400 can be a movable block or a fixed block. The distancebetween the First Beam Expander block 400 and the Movable Beam Expanderblock 500 can be adjusted e.g. by a position actuator.

As was illustrated already in FIGS. 2A-B, as the focal point is movedaway from its optimal position in the target tissue, the aberrationsincrease. These aberrations are typically called “geometricaberrations”, as they can be understood from tracing geometric rays, andoriginate from the finite extent of the lenses. These geometricaberrations can be limited by making a numerical aperture of the ZScanner 450 smaller. As such, the geometric aberrations depend both onthe Z focal depth and the numerical aperture NA.

In addition, with decreasing numerical aperture NA, a second source ofaberrations arises from the wave nature of light. These aberrations giverise to the so-called “diffraction aberration”. This second type ofaberration increases the focal spot radius with decreasing numericalaperture.

FIGS. 12A-B illustrate the geometric and diffraction aberrations in ananterior segment of an eye as a function of the aperture size of the ZScanner 450, characterized by one of the above aberration measures: thefocal spot radius r_(f). Since the geometric aberration increases withthe aperture size while the diffraction aberration decreases, a totalaberration, defined as a sum of these two aberrations, exhibits anoptimal minimum value at an optimal aberration and corresponding optimalnumerical aberration NA_(opt).

Here the usual definition connects the numerical aperture NA and theaperture size: NA=n*Sin Ar Tan(aperture size/(2*focal length)), where nis the refractive index of the material in which the image is formed.

These curves are for specific Z focal depths, 1 mm Z focal depth in FIG.12A and 8 mm Z focal depth in FIG. 12B. As the geometric aberration isdifferent at different Z focal depths, the minimum of the totalaberration curve and thus the optimal aperture size and the optimalnumerical aperture NA_(opt) of the whole system depend on the Z focaldepth: NA_(opt)=NA_(opt)(z). In particular, the optimal aperture sizeand NA_(opt) decreases for increasing Z focal depth, from 32 mm to 25 mmin this specific instance as the Z focal depth increases from 1 mm to 8mm. Therefore, laser delivery systems which are intended to be used forboth corneal and lens surgeries, need to cover a broader range ofapertures and corresponding NA ranges. This requirement posesconsiderable design challenges.

As discussed further below, FIGS. 12 A-B also illustrate that theaberration exhibits a broad flat optimum for the typical corneal Z focaldepths of 1 mm, while it exhibits a narrower, sharper minimum for Zfocal depths typical for lens-surgery.

The aberration can be also characterized by the other three aberrationmeasures S, ω, or a₄₀ as well, all yielding curves exhibiting anoptimum. Any of the above four aberration measures can correspond to anyof the five reference points P(1), . . . P(5) described above, or can bean average taken over some or all of these reference points, or maycorrespond to other reference points.

In some implementations, in a wide range of Z focal depths, the aperturesize and the corresponding NA can be adjusted to essentially the optimalnumerical aperture NA_(opt)(z), minimizing the total aberration,measured by an aberration measure. This functionality allows a strongreduction of the total aberration. Here, as before, the aberrations canbe measured by one of the four aberration measures r_(f), S, ω, or a₄₀,at any one of the above five reference points P1, . . . P5. The optimalaberration corresponds to a minimum of aberration measures r_(f), ω, ora₄₀, or a maximum of the Strehl ratio S.

In some other implementations, where the optimal aberration may not bereached, or design considerations dictate that an aberration away fromthe optimal value should be used, the Movable Beam Expander Block 500can still decrease the values of the aberration measures r_(f), ω, ora₄₀ by at least a P(MovableExpander) percentage, or correspondinglyincrease the value of the Strehl ratio S by at least aP(MovableExpander) percentage, compared to the aberration measures of anessentially identical laser system where the second block of the ZScanner 450 is not movable and thus the numerical aperture is notadjustable. In some implementations P(MovableExpander) can be 20%, 30%,40%, or 50%. Here, as before, the aberration measures r_(f), S, ω, ora₄₀, can be measured at any one of the five reference points P1, . . .P5.

In some implementations, laser systems having the Z Scanner 450 with theadjustable numerical aperture NA can increase the Strehl ratio S above0.8, relative to essentially identical laser systems where the Z scannerdoes not have an adjustable numerical aperture, having a Strehl ratio Sbelow 0.8.

An additional design challenge is not only to minimize the totalaberration at a fixed Z focal depth by adjusting the laser deliverysystem to its optimal aperture size and corresponding numerical apertureNA_(opt)(z), but also to keep the system at least close to the Zdependent optimal numerical aperture NA_(opt)(z) as the Z focal depth isscanned. In a typical implementation, the optimal numerical aperturedecreases as the focal depth increases.

To address this variation of the optimal aperture as the Z focal depthis scanned within the Z scanning range, implementations of the laserdelivery system 1 have the capability of changing the numerical apertureNA(z) as a separate parameter of the Z Scanner 450, essentiallyindependently from varying the Z focal depth itself.

Implementations, where two quantities are controlled essentiallyindependently, as presently the Z focal depth and the numerical apertureNA, typically have a pair of control parameters to achieve thismodality. Examples include the pairing of a controllable distancebetween the First Beam Expander block 400 and the Movable Beam Expanderblock 500 and a position of a movable lens in either of these blocks,which can be adjusted by a secondary optical controller. Another exampleincludes two movable lenses in any combination in the two blocks of theZ Scanner 450. It is recalled that the First Beam Expander block 400 canbe implemented as a fixed block or a movable block.

In some implementations the numerical aperture NA can be adjusted to asequence of optimal numerical aperture values NA_(opt)(z), yielding asequence of optimal total aberration values at a sequence of Z focaldepth as the Z focal depth is scanned.

As before, the optimal total aberration can be captured by the minimumof any of the above aberration measures r_(f), ω, or a₄₀, or the maximumof the Strehl ratio S. The Z scanning ranges can be e.g. 5-10 mm or 0-15mm. The Z focal depth can be scanned at a radius r1=0 mm, or r2=3 mm, orat some other radius r, or at a variable radius r(z), bounded e.g. byr<3 mm.

Table 7 illustrates an example, where the second column describes thescanning of the Z focal depth within a Z scanning range of (−0.14 mm,11.65 mm) in an ocular target tissue and the third column shows thecorresponding values of NA_(opt)(z). Implementations of the Z Scanner450 are capable of adjusting the Z focal depth in this range andadjusting the numerical aperture NA to its optimal value NA_(opt)(z) atthese focal depths.

TABLE 7 Z Position of Movable Expander 500 [mm] Z focal depth [mm]NA_(opt)(z) 0.00 11.65 0.17 5.00 9.68 0.18 10.00 7.94 0.19 15.00 6.430.20 20.00 5.12 0.22 25.00 3.98 0.23 30.00 3.00 0.25 35.00 2.16 0.2740.00 1.44 0.28 45.00 0.83 0.30 50.00 0.30 0.32 55.00 −0.14 0.34

In some other embodiments, the Z focal depth maybe scanned within a Zscanning range of 0 mm to 10 mm. In the course of scanning the numericalaperture may vary within a range of 0.4 to 0.1, in some otherembodiments from 0.35 to 0.15.

FIG. 12C illustrates an analogous sequence of aberration curves,corresponding to a sequence of Z focal depths of 8 mm, 4 mm, 2 mm, and 0mm, exhibiting a sequence of corresponding optimal numerical aperturesN_(opt)(z).

FIG. 12D illustrates explicitly the optimal numerical aperturesN_(opt)(z) as a function of the corresponding Z focal depths.

As described above, the separate adjustability of the Z focal depth andthe numerical aperture NA typically requires two independentlyadjustable control parameters. Some implementations, however, may notoffer the separate and independent adjustability of Z and NA. Instead,for every Z focal depth, these implementations adjust automatically thenumerical aperture to either its optimal value NA_(opt)(z), or at leastto a vicinity of NA_(opt)(z), without a separate NA adjusting step by anoperator. For example, NA can track NA_(opt)(z) within a P(track)percent, where P(track) can be 10%, 20%, or 30%.

These implementations can have only a single, integrated adjustablecontroller. In the just described example, this integrated controllermay only display to a user of the system that it controls the Z focaldepth in the target region. However, the controller may contain acoupled aperture adjuster, which simultaneously adjusts the numericalaperture NA to track NA_(opt)(z) without a separate tuning stepperformed by the user of the laser delivery system 1.

In some implementations adjusting the distance between the First BeamExpander 400 and the Movable Beam Expander 500 may perform thisfunctionality adequately. In other implementations, a single movablelens can offer this modality. In yet other implementations, acombination of two adjusters may be employed.

These implementations offer a simplified control function for theoperator of the laser delivery system 1. Since achieving such a single,integrated control function is a design challenge, some implementationsperform these integrated control functions in combination with the otherblocks, such as the Precompensator 200, the XY Scanner 300 and theObjective 700.

In some implementations, where the optimal total aberration valuescannot, or are not, achieved for various design considerations, thenumerical aperture NA can be adjusted to a sequence of numericalaperture values at a sequence of Z focal depths along the Z scanningpath within the Z scanning range to reduce the total aberration by atleast a P(scan) percentage relative to laser systems whose Z Scanner 450does not have an adjustable numerical aperture NA. In someimplementations P(scan) can be 20, 30, 40, or 50 percent.

As before, the total aberration can be characterized by any on of thepreviously introduced aberration measures r_(f), ω, or a₄₀.Equivalently, the reduction of the aberration can be characterized by acorresponding increase of the Strehl ratio S. The Z scanning path can bea path parallel to the Z axis at a radius R from the optical, or Z axisof the laser system. In some implementations the Z scanning path can belocated between radii r1=0 mm and r2=3 mm from the optical Z axis.

The total aberration can be measured in several different ways. Thetotal aberration can refer to a total aberration averaged over the Zscanning path, or to the maximum or minimal value of the totalaberration along the scanning path. The reduction of the totalaberration can refer to any one of these possibilities.

In some implementations, the numerical aperture NA can be adjusted froma first value when a corneal procedure is performed to a second valuewhen an anterior segment procedure is performed. In some implementationsthe first value is in the range of 0.2-0.5 and the second value is inthe range of 0.1-0.3. In some other implementations the first value canbe in the range of 0.25-0.35 and the second value can be in the range of0.15-0.25.

The present implementation of the Z Scanner 450 is different fromexisting corneal laser delivery systems in several other ways, includingthe following.

1. In corneal laser delivery systems it is typically required that thenumerical aperture does not change during the Z scan of the focal depthto ensure the simplicity of the design. This design is satisfactory forcorneal surgery as the total aberration induced by the typical 1 mm Zscan is not a serious limiting factor of the precision of the corneallaser delivery systems. In contrast, implementations of the laserdelivery system 1 have a variable numerical aperture NA to keepadjusting the aperture to its optimal aperture over the extensivesurgical Z interval of e.g. 5-10 mm. This, of course, is achieved by themodality of the numerical aperture NA being adjustable essentiallyindependently from the Z focal depth.

2. Also, typical existing corneal systems have their Z scanner in theObjective 700, or as a part of a complex implementation of the Objective700, whereas the present Z Scanner 450 is disposed before the Objective700. Here the Objective 700 denotes the final lens group of the laserdelivery system 1 which is disposed in a functional mechanical housingseparate from the functional mechanical housing of the XY Scanner andthe Z Scanner. The term functional mechanical housing refers not to theoverall housing of the delivery system, whose design can be dictated byergonomic or appearance considerations, but to the housing which isholding together the lenses to perform their actual optical function.The Objective 700 of the present implementations is typically positionedin the optical pathway after the XYZ scanning beam, outputted by the ZScanner 450, is deflected by the mirror 600.

3. FIGS. 12A-B illustrate a further challenge in the design oflens-surgical optical systems. Visibly, the total aberration exhibits awide, flat optimal region for typical corneal Z focal depths of 1 mm,thus (i) the system parameters can be optimized for otherconsiderations, (ii) a broad Z scanning range can be used, and (iii)less precise tuning of the system parameters is needed, all without muchdeterioration of the focal spot size. In contrast, for lens-surgicalsystems the focal spot size deteriorates quickly when (i) the systemparameters are optimized for other considerations, (ii) a broader Zscanning range is implemented, and (iii) the system parameters are tunedless precisely.

In a further aspect of the embodiments of the Z Scanner 450, it isrecalled that laser delivery systems which include an imaging sub-systemor a visual observational optics sub-system, have the beams associatedwith either of these sub-systems coupled into the laser delivery system1 through the mirror 600. The mirror 600 can be a dichroic mirror, forexample. In typical surgical systems the Objective 700 refers to thelens group which is positioned after the mirror 600 in the opticalpathway.

Implementing the Z Scanner 450 before the mirror 600 and separate fromthe Objective 700 is an important design consideration also because theweight of the Objective 700 is a critical factor, since the Objective700 makes essentially direct contact with the target tissue, such as theeye of the patient. Therefore, minimizing the weight or mass of theObjective 700 makes implementations of the laser delivery system 1impose a reduced pressure on the eye. And since this pressure deformsthe eye itself and thus decreases the precision of the surgicalprocedure, designs which reduce the pressure on the eye increase theprecision of the ophthalmic surgery considerably.

Tables 8-9 illustrate ranges of some relevant parameters for variousembodiments of the First Beam Expander block 400 and the Movable BeamExpander block 500. The Beam Expander blocks each can have 2-10 lenses,in some embodiments 3-5 lenses, which are configured to carry out theabove functionalities.

Table 8 illustrates a five lens embodiment of the First Beam Expanderblock 400 using an industry standard convention, describing groups ofthick lenses in terms of the individual surfaces. First Beam Expanderblock 400 can include lenses 411, 412, 413, 414 and 415 with parametersin the following ranges (indicated by brackets):

TABLE 8 Surface Curvature [1/m] Distance [mm] Refractive Index n 1   (0,1.5) (5, 25)  (1.6, 1.93) 2 (22, 28) (12, 22)  (1.6, 1.7) 3 (−17, −14)(0.5, 12)   1 4 (7.0, 8.5) (15, 29)  (1.65, 1.8)  5 (−19, −13) (3, 14) 16 (14, 18) (8, 12) (1.6, 1.7) 7   (0, 9.3) (6, 12) 1 8 (−28, −21) (1,5)  (1.65, 1.75) 9 (−15, −6) 

In some embodiments, the First Beam Expander block 400 includes,sequentially from an input side facing the XY Scanner 300: a first lensgroup with a positive refractive power, a meniscus lens, having a convexsurface facing the input side, and a second lens, having a concavesurface facing the input side.

Other implementations are related to the implementations of Table 8 by ascale factor a, having five scaled lenses, the curvatures of the secondcolumn being multiplied by a, the distances of the third columnmultiplied by 1/a, and having unchanged indices of refraction n. Thescale factor a can assume values between 0.3 and 3.

Table 9 illustrates a four lens embodiment of the Moving Beam Expanderblock 500, including lenses 511, 512, 513, and 514, with parameters inthe following ranges:

TABLE 9 Surface Curvature [1/m] Distance [mm] Refractive Index n 1 (−25,−10) (3, 7) (1.7, 1.8) 2 (−25, −28) (0, 2) 1 3 (−43, −24) (1.5, 5)   (1.5, 1.62) 4  (8.5, 19.4) (26, 31) 1 5 (−6.2, −4.6) (10, 16) (1.53,1.6)  6 (−18.4, −14.7) (34, 49) 1 7 (1.9, 4.2)  (8, 14) (1.58, 1.61) 8 (−11, −9.0)

Some implementations of the Movable Beam Expander block 500 include,sequentially from an input side facing the First Beam Expander block400: a meniscus lens, having a concave surface facing the input side, anegative lens with a negative refractive power, and a positive lensgroup with a positive refractive power.

Other implementations are related to the implementations of Table 9 by ascale factor a, having four scaled lenses, having the curvatures of thesecond column being multiplied by a, the distances of the third columnmultiplied by 1/a, and having unchanged indices of refraction n. Thescale factor a can assume values between 0.3 and 3.

FIGS. 13A-B illustrate embodiments of Tables 8-9 in two configurationswith different distances between the First Beam Expander block 400 andthe Moving Beam Expander block 500. In some implementations, the MovingBeam Expander block 500 can be moved relative to the First Beam Expanderblock 400 by a distance in the range of d=5-50 mm.

These figures illustrate the design considerations of the Z Scanner 450at work.

FIG. 13A illustrates the case when the Movable Beam Expander block 500is in a position relatively far from the First Beam Expander block 400.In this case the beam exiting the combined assembly has (i) convergentrays, (ii) a relatively large diameter at an exit pupil ExP, (iii) ashallower Z-depth of the focal spot when a fixed focal length objectiveis placed near the exit pupil of the Z Scanner 450, and thus (iv) thefocal spot is formed by a beam with a higher numerical aperture NA.

FIG. 13B illustrates the case when Movable Beam Expander block 500 iscloser to the First Beam Expander 400 than in the case of FIG. 13A. Herethe beam has (i) divergent rays, (ii) a smaller diameter at the exitpupil ExP, (iii) a deeper Z-depth of the focal spot when a fixed focallength objective is placed at the exit pupil of the Z Scanner 450, andthus (iv) the focal spot is formed by a beam with a smaller numericalaperture NA.

In summary, at shallower Z focal depths the focal spot is created by alarge NA beam, whereas for increasing Z focal depths the numericalaperture NA decreases. The relative change in the numerical aperture NAcan be optimized by optimizing the location of the exit pupil ExP of theBeam Expander blocks 400 and 500 and the location of the entrance pupilof the focusing Objective 700. These implementations are alternativeways for optimizing the numerical aperture at different focal depthseven without use of the functionalities of the pre-compensator 200.

As discussed above, the numerical aperture NA can be extensivelyadjusted with or without the Precompensator 200. In the overall laserdelivery system 1 the numerical aperture NA can be adjusted bycontrolling the Precompensator 200, the First Beam Expander block 400 orthe Movable Beam Expander block 500, or by controlling these blocks incombination. The actual choice of implementation in practice depends onother higher level system level requirements, such as scanning range,scanning speed, and complexity. Implementations with other numericalranges can also be configured to perform some or all of the abovedescribed functionalities.

FIG. 14 illustrates a further aspect of the Z Scanner 450. Threedifferent characteristic beams are shown, emanating from an exit pivotpoint PP(XY) of the XY Scanner 300. Remarkably, all three characteristicbeams are focused into an entrance pivot point PP(O) of the Objective700 by the Z Scanner 450. The position of PP(O) can be adjusted e.g. bymoving the Movable Beam Expander 500.

As discussed below, laser delivery systems which generate a pivot pointPP(O) located off the mirrors of the XY Scanner 300 have useful featurese.g. in embodiments where the PP(O) pivot point falls inside theObjective 700.

In other embodiments, the XY Scanner 300 has an exit pivot point PP(XY)farther than the distance to the Z Scanner 450. In these embodiments,the Z Scanner 450 only modifies the exit pivot point PP(XY) of the XYScanner 300 into the entrance pivot point PP(O) of the Objective 700.

In either case, these implementations make use of the existence of anintermediate focal plane 451, located between the First Beam Expanderblock 400 and the Movable Beam Expander block 500. The existence of thisintermediate focal plane 451 is indicated by the focal points of thethree characteristic beams lining up laterally with essentially the samez coordinate. Conversely, implementations which do not possess such anintermediate focal plane are not well suited to have an adjustable pivotpoint PP(O).

5. Objective 700

In some implementations the laser beam outputted by the Z Scanner 450 isdeflected by the Beam Splitter/Dichroic Mirror 600 onto the Objective700. Through this mirror 600 various auxiliary lights can also becoupled into the laser delivery system 1. The auxiliary light sourcescan include light associated with an optical coherence tomographyimaging (OCT) system, an illumination system and a visual observationalblock.

The Objective 700 can provide a shared optical pathway for an XYZscanned laser beam, propagating from the laser engine 100 through the XYScanner 300 and the Z Scanner 450, and the auxiliary light into thesurgical target region. In various implementations, the Objective 700may include objective lens groups. In several implementations the lensesof the objective lens groups do not move relative to each other. Assuch, while the Objective 700 is an integral part of the Z scanningfunctionality, it does not contribute to the Z scanning in a variable ordynamic manner. In these implementations no lens position is adjusted inthe Objective 700 to move the Z focal depth of the focal spot.

Implementations of the Objective 700 can control at least one of aspherical aberration, coma, and higher order aberrations of the surgicalpulsed laser beam.

Since the Objective 700 is guiding lights of different wavelength,implementations of the Objective 700 use achromatized lens groups. Thewavelength of the auxiliary light can be e.g. in the range of 0.4 micronto 0.9 micron, and the wavelength of the surgical light can be in the1.0-1.1 micron range. Implementations of the Objective 700 keep thechromatic aberrations below a predetermined value throughout the rangeof wavelengths of the used lights, such as 0.4 micron to 1.1 micron inthe above example.

The weight or mass of the Objective 700 is an important consideration.In some implementations the objective is in mechanical contact with theeye of the patient. As such, it exerts pressure on the eye. Thispressure can distort the eye from its relaxed configuration, making itmore difficult to select targets and direct the surgical laser beamaccurately.

Furthermore, if the patient moves during the surgical procedure, it maybe preferable that the objective can move with the smallest resistancein response to the patient's movement. Although the weight of theobjective can be statically balanced with a spring system orcounterbalance, these measures may not reduce the dynamic or inertialforces. In fact, these forces may be increased by such measures. All ofthese considerations point toward the usefulness of reducing the weightor mass of the Objective 700.

There are numerous ways to identify critical forces and correspondingobjective masses in relation to eye surgical procedures. A review ofvarious impacts on the eye was published e.g. in Determination ofSignificant Parameters for Eye Injury Risk from Projectiles; Duma S M,Ng T P, Kennedy E A, Stitzel J D, Herring I P, Kuhn F. J Trauma. 2005October; 59(4):960-4. This paper reviewed objects impacting an eye andprovided critical energy values of the impacting objects, correspondingto (i) different types of damage to the eye, including minor injurieslike corneal abrasions, moderate ones like lens dislocations, and graveinjuries like retinal damage. The paper also assigned a probability ofinjury, from (ii) low, representing a few percent chance, to medium,representing an about 50% chance, to high, referring to a near certaintyof injury. The paper further classified (iii) the impact scenariosaccording to the shape of the impacting object, categorizing accordingto total impacting energy and impacting energy normalized by the impactarea.

These results can be applied to the specific case of eye surgery byinvestigating the possibly highest impact injury, caused by a totalbreakdown of the mechanical support system of the Objective 700. Such abreakdown may result in a freefall of the entire Objective 700 over atypical vertical path of 20-25 mm, transferring all of the objective'senergy to the eye itself. Critical masses can be computed from thepublished critical energy values modeling the freefall of the objectiveaccording to known physical principles.

A vertical path of this length can emerge from the following designprinciples. The Objective 700 can be mounted on a vertical sliding stageto provide a safe and reliable docking of the laser delivery system 1 bya gantry to the eye. Such designs ease precision and force requirementson the gantry because the vertical gantry accommodates the Objective 700to be positioned within the vertical travel range. Further, once the eyeis docked, these designs allow the eye to move vertically relative tolaser source 100 without breaking the attachment of the eye to the laserdelivery system 1. These movements may occur due to movement of thepatient or movement of the surgical bed. A vertical travel range of 20to 25 mm of the Objective 700 mitigates effectively and safely againstgantry forces and patient motion within this range.

Finally, (iv) a design consideration also influences the critical massesin the sense that the (“optical”) mass of the optical elements of theObjective 700, such as the glass lenses alone in the objective lensgroups define a lower bound on the mass of the entire objective, asthere are numerous ways to reduce the mass of the housing and thecontrol systems of the objective, while it is much harder to reduce themass of the lenses. In present systems the total mass of the objectivecan be two-three times the “optical” mass of the lenses alone.

Some of these criteria yield sharper definitions of critical masses,others only a smooth crossover dependence, not lending themselves to asharp definition.

From all the possible combinations of the above (i)-(iv)classifications, four relatively sharp and meaningful definitions ofcritical masses MC can be identified as follows:

(1) MC1˜400 grams: objectives with masses M<MC1 pose essentially no riskof injury for a patient even in a worst case breakdown scenario;

(2) MC2˜750 grams: masses in the MC1<M<MC2 regime can have a larger than10% chance of causing some corneal abrasions via the total impactingenergy;

(3) MC3˜1,300-1,400 grams: masses in the MC2<M<MC3 regime may have a 50%chance of causing corneal abrasions in any impacting scenario; andfinally

(4) MC4˜3,300 grams: masses in the MC3<M<MC4 range in some impactingscenarios can cause a near certain corneal abrasion, and can develop anon-zero chance of injuries of medium severity or worse.

All of these probabilities, of course, are to be multiplied with thesmall probability of the total breakdown of the mechanical supportsystem of the objective actually occurring. However, in ophthalmicapplications extreme measures need to be taken to guard against allconceivable injury scenarios, however unlikely, making the abovecritical masses relevant.

Therefore, the above considerations identify four critical massesaccording to clear criteria, regarding total and optical masses of theObjective 700. Accordingly, embodiments of the Objective 700 where thedesign process manages to reduce the objective mass below any one of theabove critical masses MC4, . . . , MC1, offer qualitatively betterchances for safe surgical procedures.

Existing objectives for femtosecond ophthalmic lasers have a mass above5000 grams, considerably above even the largest of these four criticalmasses. An exception is US patent application 20030053219 by Manzi,which describes a lens system where the optical mass of the lenses aloneis about 1000 grams, possibly leading to a total mass of 2,000-3,000grams. While Manzi's design is lighter than other existing objectives,it is still quite massive. This is primarily due to a Z scanner being anintegral part of the objective since lens elements inside the objectiveare used for Z focus control. Additional mass is required by Manzi forthe precision machined housing, for a precision linear guide for thelenses, and for a servo motor, all increasing the total mass to valuesback above 5000 grams.

In contrast, a mass of various embodiments of the Objective 700 can fallin any of the above four mass ranges: 0-400 grams, 400-750 grams,750-1,350 grams, and 1,350-3,300 grams. The mass can be either theoptical or the total mass. E.g. the lenses in an implementation of theObjective 700 can have a mass of less than 130 grams. It is feasible tomount these lenses in a precision metal housing for a total assemblymass of 400 grams.

Embodiments of the Objective 700 achieve such a remarkable massreduction to below 400 grams, 750 grams, 1,350 grams and 3,300 grams byremoving the Z scanning functionality to the separate Z Scanner 450,housing it in a separate functional or mechanical housing. Here the term“functional or mechanical housing” refers to the fact that overall,non-functional design considerations may result in disposing theseparate Z Scanner 450 into the same general container as the Objective700, but such a general container does not serve an optical function ormechanical purpose.

In some embodiments, a mass of the Objective 700 can be reduced by aP(mass) percentage in comparison to analogous objectives, which performat least some of the dynamic Z scanning functionality by adjusting anoptical characteristic of the Objective 700. Such characteristic can bethe entire Z Scanner 450 being integrated into the Objective 700, or theMovable Beam Expander block 500 being integrated into the Objective 700,or one or more movable scanning lens being integrated into the Objective700. P(mass) can be 10%, 50%, or 100%.

Another related aspect of the Objective 700 and the corresponding designof the surgical laser system 1 was described in relation to FIG. 14,where it was shown that embodiments of the Z Scanner 450 can focus theXYZ scanned laser beam onto the objective's entrance pivot point PP(O).Embodiments, which have the entrance pivot point PP(O) inside theObjective 700 have a much-reduced beam radius rb over a large fractionof the optical pathway, as the beam converges towards this internalpivot point PP(O). In turn, a beam with a reduced beam radius rb can becontrolled by smaller lenses, resulting in significant reduction of theoverall mass of the Objective 700.

An implementation of the Objective 700 according to the above designinsights is summarized in Table 10 and illustrated in FIG. 15.Implementations of the Objective 700 include a first lens group, toreceive the surgical pulsed laser beam from the Z Scanner 450, and asecond lens group, to receive the surgical pulsed laser beam from thefirst lens group and to focus the surgical laser beam onto a targetregion.

Table 10 illustrates the Objective 700 of FIG. 15 in more detail viasurfaces 1 trough 16. The Objective 700 has nine lenses L1-L9 andinterfaces with the Patient Interface 800 via surface 17. As before, thebrackets indicate the ranges the corresponding parameters can assume.(Surfaces 1 and 2 define a doublet of lenses L1/L2 and surfaces 8 and 9define a doublet of lenses L5/L6, hence the 16 surface instead of 18.)

TABLE 10 Surface Curvature [1/m] Distance [mm] Index of refraction n 1(−1.5, 4.5)   (1, 6) (1.7, 1.9) 2 (7.8, 45)  (6.4, 13)  1.56, 1.8)  3(−4.2, 3.2)     (0, 3.2) 1 4 (22, 36) (10.5, 14)   (1.47, 1.62) 5 (−10,5)      (0, 6.8) 1 6 (−27.2, −12.6)  (8.0, 11.6) (1.58, 1.63) 7 (−30.3,2.5)      (0, 6.7) 1 8 (−3.1, 18.9) (4.0, 8.3) (1.65, 1.76) 9 (40.7,72)    (8.2, 17.9) (1.57, 1.69) 10 (−28.3, −22.1) (0, 3) 1 11 (−37.8,−17.6) (3.0, 26)  (1.70, 1.86) 12 (−6.3, 14.0)   (0, 3.0) 1 13 (37.9,65)   (12.0, 22.3) (1.54, 1.72) 14 (−15.4, 5.2)      (0, 6.5) 1 15(−55.1, −21.6) (2.0, 4.7) (1.56, 1.85) 16 (11.4, 26.8)   (0, 2.0) 1 17(−60.0, 0)    (1.0, 1.5) (1.47, 1.54)

In other implementations, different number of lenses can be used withdifferent parameter ranges, which satisfy the above designconsiderations comparably well.

In some implementations the Objective 700 can be described in terms oflens groups. For example, the Objective 700 can include a first lensgroup, to receive the XYZ scanned laser beam from the Z Scanner 450, anda second lens group, to receive a laser beam from the first lens group.The second lens group can include a first lens with an index ofrefraction in the range of 1.54 to 1.72, an entry surface with acurvature in the range of 37.9 to 65 l/m and an exit surface with acurvature in the range of −15.4 to 5.2 l/m. Further, the second lensgroup can also include a second lens, separated from the first lens by adistance in the range of 0 to 6.5 mm, with an index of refraction in therange of 1.56 to 1.85, an entry surface with a curvature in the range of−55.1 to −21.8 l/m and an exit surface with a curvature in the range of11.4 to 26.8 l/m. The Objective 700 can output the laser beam onto thepatient interface 800 through the second lens.

In some implementations an effective focal length of the Objective 700is less than 70 mm.

In some embodiments a distance from the Objective 700 to the patientinterface 800 is less than 20 mm.

In some designs a curvature of a focal plane of the laser deliverysystem 1 is larger than 20 l/m.

Numerous other implementations of the Objective 700 and the entiresurgical laser system 1 can be also created to adhere to the designprinciples expressed throughout this application by using commerciallyavailable optical design software packages such as Zemax from ZemaxDevelopment Corporation or Code V from Optical Research Associates.

6. Overall System Optical Performance

In the various implementations, the parameters of the subsystemsPrecompensator 200, XY Scanner 300, Z Scanner 450 and Objective 700 canbe optimized in an interdependent manner so that the optical performanceof the overall laser delivery system 1 may exhibit properties which areuniquely useful for e.g. ophthalmic surgical applications.

Tables 11A-B summarize the optical performance of the overall laserdelivery system 1 in a first and a second implementation in terms of thenumerical aperture NA and the Strehl ratio S. The optical performance isagain characterized at reference points, in analogy to the abovereference points P1, . . . P5. Tables 11A-B show the optical performanceof the laser delivery system 1 with its components in configurations A,B, C, and D, delivering the laser beam to a center of the cornea (A), aperiphery of the cornea (B), a center of the lens (C) and a periphery ofthe lens (D), respectively. These reference points represent a largesurgical volume, associated with the challenge of performing ophthalmicsurgery on the crystalline lens.

Tables 11A-B show the radial coordinates of the reference points havingspecific values. However, in other embodiments NA and S assume values inthe same respective ranges “around” these specific radial coordinates.In some cases the term “around” refers to a range of radial coordinateswithin the P(radial) percent of the shown radial coordinate values,where P(radial) can be one of 10%, 20% and 30%. E.g. points having a zradial coordinate in the range of 7.2 mm and 8.8 mm are within theP(radial)=10% vicinity of the z=8.0 mm radial coordinate of the “lens,center” reference point.

Furthermore, in some embodiments, NA and S fall in only one of theirthree respective ranges listed for the B, C, and D configurations. Insome other embodiments, NA and S fall into two of their three respectiveranges, listed for the B, C, and D configurations in Tables 11A-B.

Visibly, the described laser delivery system is well corrected toessentially a diffraction limited optical performance throughout theentire lens-surgical volume.

TABLE 11A Tissue, Depth z Radius r Numerical Strehl Configurationlocation [mm] [mm] aperture NA ratio S A Cornea, 0.3 0 (0.25, 0.40)(0.90, 1.0) center B Cornea, 0.3 6.2 (0.25, 0.40) (0.90, 1.0) peripheryC Lens, 8 0 (0.15, 0.35) (0.90, 1.0) center D Lens, 7.3 4 (0.15, 0.35)(0.80, 1.0) periphery

TABLE 11B Con- Tissue, Depth z Radius r Numerical figuration location[mm] [mm] aperture NA Strehl ratio S A Cornea, 0.3 0 (0.30, 0.35) (0.95,1.0) center B Cornea, 0.3 6.2 (0.30, 0.35) (0.90, 0.95) periphery CLens, center 8 0 (0.20, 0.25) (0.95, 1.0) D Lens, 7.3 4 (0.20, 0.25)(0.85, 0.90) periphery

Analogous designs, which have a Strehl ratio S higher than 0.8 can beconsidered equivalent to the above listed designs, as all of thesedesigns are considered diffraction limited systems.

Other aberration measures, such as the focal spot radius r_(f) can bealso used besides the Strehl ratio S to characterize the overall opticalperformance of the laser delivery system 1. Since large Strehl ratioscombined with large numerical apertures NAs translate to small focalspot radii r_(f), throughout the configurations A-D the focal spotradius r_(f) can stay below 2 microns in some implementations, in othersbelow 4 microns, in yet others below 10 microns in the ocular targetregion.

To characterize the laser delivery system's performance more accurately,and to represent the substantial impact of the cornea and lens on thebeam propagation, the NA and S values of Tables 11A-B have been derivedby designing the system including the eye as an integral part of theoptical design. In some designs, the eye is modeled in its natural form.In others, a degree of applanation of the eye is included, to representauthentic surgical condition.

Table 12 summarizes a simple model of the relevant ocular tissues, asshown by Model human eye 850 in FIG. 15. (The numbering of the surfaceswas chosen to continue the numbering of Table 10, starting with surface18, the surface connecting the Patient Interface 800 to the cornealtissue.) The ocular tissue can be modeled by a 0.6 mm thick cornea(entered from the Patient Interface via shared surface 18), aqueoushumor (entered from the cornea via surface 19) and the crystalline lens(entered from the aqueous humor via surface 20). The separations of theocular surfaces are treated similarly to the separations of the lenssurfaces 1-16.

TABLE 12 Surface Curvature [1/m] Distance [mm] Index of refraction n 18(−100, −80) 0.6 1.38 19 (−100, −80) (2.0, 4.0) 1.34 20 (−100, −80) (3.0,5.0) 1.42

The NA and S values of Tables 11A-B were calculated using this model ofthe ocular tissue. Related models of the eye result in comparableaberration measures.

In a separate further aspect, in some implementations of the opticaldesign of the entire laser delivery system 1 can be simplified byleaving some of the distortions and field curvatures uncorrected byoptical means.

FIG. 16 illustrates that in some systems this design principle wouldrender the positional accuracy of the surgical system less advantageous.The square dots indicate the position of the focal spot as a mirror ofthe XY Scanner 300 scans in 1 degree steps and the Z Scanner 450 scansthe Z focal depth by moving the Movable Beam Expander 500 in 5 mm steps.Visibly, the “focal plane”, defined as the XY scanned locations of thefocal spot while the keeping the Z focal depth constant, is curved. Atthe lateral periphery the cutting depth is shallower, consistent withthe known behavior of lenses with uncorrected field curvature.

Likewise, if the mirrors of the XY Scanner 300 are kept fixed and the ZScanner 450 scans the Z focal depth, the lateral position of the focalspot changes. Further complicating the design, neither the radiallateral XY position nor the Z focal depth exhibits a linear dependenceon the respective scanner positions. In the XY plane these distortionsare called barrel or pincushion distortions. (In many implementations,the third coordinate, the azimuth angle of the XY Scanner 300 transfersunchanged to the azimuth angle of the focal positions, and hence will besuppressed.)

FIG. 17 illustrates how some implementations of the laser deliverysystem 1 offer new, computational solutions to the described challenges.The scanner coordinates are given in spherical coordinates (ζ, χ, φ),where ζ is the position of the Z Scanner 450, χ is an inclination angleof the XY Scanner 300 from the optical axis, and φ is the azimuth angle.The focal spot positions are given by the cylindrical focal coordinates(z, r, φ), z being the Z focal depth, r the radial distance from theoptical axis, and φ the azimuth angle.

The azimuth angle of the focal position can be essentially the same asthe azimuth angle of the scanners and thus is not shown. The remainingXY and the Z scanner coordinates (ζ, χ) can be discretized within theirrespective scanning intervals, defining a scanning grid and acorresponding scanner matrix C_(ij), defined as C_(ij)=(ζ_(i), χ_(j)).If the actual scanner coordinates assume a value (ζ_(i0), χ_(j0)), thenthe scanning matrix C_(ij) is 1 at this particular (i0, j0) pair andzero for all other (i, j) pairs.

Similarly, the focal spot positions can be characterized by a twodimensional focal matrix S_(kl), where S_(kl) is related to thediscretized radial and Z depth focal coordinates (z_(k), r_(l)). Interms of the scanner matrix C_(ij) and focal matrix S_(kl), the opticalperformance of the laser delivery system 1 can be characterized with afour dimensional transfer matrix T_(ijkl), which expresses how thescanner coordinates (ζ_(i), χ_(j)) transform onto the focal coordinates(z_(k), r_(l)) in general: S=TC, or in detail:

$\begin{matrix}{S_{k\; l} = {\sum\limits_{i\; j}{T_{k\; l\; i\; j}C_{i\; j}}}} & (5)\end{matrix}$

While the transfer matrix T_(ijkl) represents a linear connectionbetween the scanner matrix C_(ij) and focal matrix S_(kl), in some otherimplementations a non-linear relationship may exist between the scannermatrix C_(ij) and focal matrix S_(kl). In those implementations Eq. (5)is replaced by a non-linear connection.

The laser delivery system 1 can be designed to optimize the elements ofthe transfer matrix T by computational ray tracing, physicalcalibration, or a combination of both. An implementation of a physicalcalibration method is described in US Patent Application US20090131921,which could be used for such a purpose.

Typically, the transfer matrix T is invertible and can be used to createthe inverse transfer matrix, T⁻¹, which connects elements of the focalmatrix S_(kl) to the scanner matrix C_(ij).

Alternatively, in some embodiments the inverse transfer matrix T⁻¹ canbe determined directly by starting a computational design process withthe desired focal matrix S_(kl) in the target region and use e.g. raytracing to reconstruct the corresponding scanner matrix C_(ij).

FIGS. 17-18 illustrate such relations. These FIGS. are nomograms,illustrating which (ζ_(i), χ_(j)) scanner coordinates the XY Scanner 300or the Z Scanner 450 can be tuned to in order to focus the beam to the(z_(k), r_(l)) focal coordinates, shown on the z and r axes.

FIG. 17 shows the χ inclination angle of the XY Scanner 300,corresponding to the (z, r) focal coordinates. As an example, to achievea Z depth of z=6 mm and a radial position of r=4 mm, the dashed linesindicate that an XY scanner inclination angle of χ=6.4 degrees can beused.

FIG. 18 shows that, to achieve the same (z, r)=(4, 6) focal coordinates,a Z scanner position ζ=15.5 mm can be used. Computationally, thenomograms can be stored in a computer memory as look-up tables. Valuesin between stored look-up coordinates can be quickly determined by twodimensional linear or quadratic interpolation.

Knowledge of the transfer matrix T and its inverse T⁻¹ allow embodimentsof the laser delivery system 1 to correct the aberrations of FIG. 16 bycomputational methods instead of optical methods. These embodiments mayinclude a computational controller, which can control at least one ofthe XY Scanner 300 and the Z Scanner 450 to control an opticaldistortion of the laser delivery system 1.

FIG. 19 illustrates that, for example, if scanning along a scanningpattern with reduced optical distortion is desired in a target region,e.g. along a flat focal plane at a predetermined Z focal depth z, thecomputational controller can perform the steps of the followingcomputational control method 900:

(910): receiving at least one of input (z_(k), r_(l)) focal coordinatesand elements of a focal matrix S_(kl) corresponding to a scanningpattern with reduced optical distortion in the target region;

(920): computing, or recalling from a stored memory at least one of the(ζ_(i), χ_(j)) scanner coordinates and the elements of the scannermatrix C_(ij), corresponding to the input (z_(k), r_(l)) focalcoordinates or elements of the focal matrix S_(kl), using apredetermined inverse transfer matrix (T⁻¹)_(ijkl); and (930):controlling at least one of the Z Scanner 450 and the XY Scanner 300according to the computed (ζ_(i), χ_(j)) scanner coordinates to scan thefocal spot according to the input (z_(k), r_(l)) focal coordinates orelements of the focal matrix S_(kl).

Laser delivery systems having such a computational controller can reducean optical distortion relative to the same or similar laser systemswithout such controllers. The degree of reduction may be as much as 10%in some embodiments, and as much as 30% in other embodiments.

The reduced optical distortion can be any one of an aberration, a fieldcurvature, a barrel distortion, a pincushion distortion, a curved focalplane, and a bent scanning line, intended to be parallel to the Z axis.

In some implementations, the computational controller performs thesefunctions in cooperation with the other blocks of the laser deliverysystem, including the Precompensator 200, the XY Scanner 300, the ZScanner 450 and the Objective 700, possibly utilizing any of their abovedescribed features.

The number of possible analogous implementations is very large, relyingon the principle of computational control to reduce optical aberrations.E.g. the computational controller in some embodiments can be capable toscan the focal spot over a focal plane with a curvature below a criticalcurvature value. In some other implementations surfaces withpredetermined shapes can be scanned with an appropriate operation of thecomputational controller.

While this document contains many specifics, these should not beconstrued as limitations on the scope of an invention or of what may beclaimed, but rather as descriptions of features specific to particularembodiments of the invention. Certain features that are described inthis document in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or a variation of a subcombination.

A number of implementations of imaging-guided laser surgical techniques,apparatus and systems are disclosed. However, variations andenhancements of the described implementations, and other implementationscan be made based on what is described.

1. A laser system for ophthalmic surgery, comprising: a laser source toproduce a surgical pulsed laser beam; an XY scanner to XY scan thesurgical pulsed laser beam in transverse directions; a Z scanner, to Zscan the XY scanned surgical laser beam along an optical axis; one ormore auxiliary optical unit, generating auxiliary light; and anobjective, to provide a shared optical pathway for the XYZ scannedsurgical laser beam and the auxiliary light through an objective lensgroup into a surgical target region; wherein the lenses of the objectivelens group do not move relative to each other; and the objective has nodynamic Z scanning function.
 2. The laser system of claim 1, wherein:the objective is configured to control at least one of a sphericalaberration, coma, and higher order aberrations of the surgical pulsedlaser beam.
 3. The laser system of claim 1, wherein: the auxiliaryoptical unit comprises an optical coherence tomography imaging system.4. The laser system of claim 1, wherein: the auxiliary optical unitcomprises an illumination light.
 5. The laser system of claim 1,wherein: the auxiliary optical unit comprises a visual observationalblock.
 6. The laser system of claim 1, wherein: the objective isconfigured to focus the XYZ scanned laser beam and the auxiliary lightonto the surgical target region in a range of wavelengths encompassingthe wavelength of the XYZ scanned laser beam and the auxiliary light. 7.The laser system of claim 6, wherein: the range of wavelength comprisesthe range of 0.4 microns to 1.1 microns.
 8. The laser system of claim 1,wherein: a mass of the objective is less than one of 400 grams, 750grams, 1,300 grams and 3,300 grams.
 9. The laser system of claim 1,wherein the objective comprises: a first lens group, to receive the XYZscanned laser beam from the Z scanner; and a second lens group, toreceive a laser beam from the first lens group, the second lens groupcomprising a first lens with an index of refraction in the range of 1.54to 1.72, an entry surface with a curvature in the range of 37.9 to 65l/m and an exit surface with a curvature in the range of −15.4 to 5.2l/m; a second lens, separated from the first lens by a distance in therange of 0 to 6.5 mm, with an index of refraction in the range of 1.56to 1.85, an entry surface with a curvature in the range of −55.1 to−21.8 1l/m and an exit surface with a curvature in the range of 11.4 to26.8 l/m; wherein the second lens is configured to output the laser beamfrom the objective onto a patient interface.
 10. A laser system forophthalmic surgery, comprising: a laser source to produce a pulsed laserbeam; an XY scanner to scan the pulsed laser beam in transversedirections; a Z scanner, to scan a focal spot of the pulsed laser beamalong an optical axis; and an objective, to focus the scanned pulsedlaser beam onto a focal spot in a target region, having an internalentrance pivot point.
 11. The laser system of claim 10, wherein: a massof the objective is less than one of 400 grams, 750 grams, 1,350 gramsand 3,300 grams.
 12. The laser system of claim 10, wherein: an effectivefocal length of the objective is less than 70 mm.
 13. The laser systemof claim 10, wherein: a distance from the objective to a patientinterface is less than 20 mm.
 14. The laser system of claim 10, wherein:a curvature of a focal plane of the laser system is larger than 20 l/m.15. The laser system of claim 10, wherein the objective comprises: afirst lens group, to receive the surgical pulsed laser beam from the Zscanner, and a second lens group, to receive the surgical pulsed laserbeam from the first lens group, the second lens group comprising: afirst lens with an index of refraction in the range of 1.54 to 1.72, anentry surface with a curvature in the range of 37.9 to 65 l/m and anexit surface with a curvature in the range of −15.4 to 5.2 l/m; a secondlens, separated from the first lens by a distance in the range of 0 to6.5 mm, with an index of refraction in the range of 1.56 to 1.85, anentry surface with a curvature in the range of −55.1 to −21.8 l/m and anexit surface with a curvature in the range of 11.4 to 26.8 l/m; and thesecond lens outputs the surgical pulsed laser beam from the objectiveonto a patient interface.
 16. A laser system for ophthalmic surgery,comprising: a laser engine, to generate a pulsed laser beam; an XYscanner to scan the pulsed laser beam in XY transverse directions; a Zscanner, to scan a focal spot of the pulsed laser beam along a Z axis;and an objective, having a mass of less than 3,300 grams.
 17. The lasersystem of claim 16, wherein: a mass of the objective is less than 1,350grams.
 18. The laser system of claim 16, wherein: a mass of theobjective is less than 750 grams.
 19. The laser system of claim 16,wherein: a mass of the objective is less than 400 grams.
 20. The lasersystem of claim 16, wherein: the mass of the objective is one of anoptical mass and a total mass.
 21. The laser system of claim 16,wherein: the objective does not scan a Z focal depth of the focal spot.22. The laser system of claim 16, wherein: the objective has an entrancepivot point inside the objective.